Do i imagine the linear (straight line) homotopy in a correct way?












1












$begingroup$


Today i learned about the linear homotopy which says that any two paths $f_0, f_1$ in $mathbb{R}^n$ are homotopic via the homotopy $$ f_t(s) = (1-t)f_0(s) + tf_1(s)$$



Am i right in imagining the given homotopy as something like this?



enter image description here



such that $F(s,t) = f_t(s) $ are simply the linesegments going from $f_0(s)$ towards $f_1(s)$ as the straight lines (which "connect" $f_0$ and $f_1$ for every $sin [0,1]$) as drawn in the picture?



Sorry if this question might be a trivial one, i just want to make sure i don't get things wrong.



Thanks for any kind of feedback!






algebraic-topology homotopy-theory path-connected







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    It's correct. Furthermore, any point $s$ moves along its straight line at constant speed.
    $endgroup$
    – Lukas Kofler
    1 hour ago










  • $begingroup$
    isn't the point $t$ rather moving along its straight line? to me, $s$ is the parameter moving along the lines from $x_0$ to $x_1$ whereas $t$ moves along the straight linesegments between $f_0$ and $f_1$
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    That's what I was trying to say, sorry -- a fixed point $f_0(s)$ moves at constant speed as $t$ varies.
    $endgroup$
    – Lukas Kofler
    1 hour ago
















1












$begingroup$


Today i learned about the linear homotopy which says that any two paths $f_0, f_1$ in $mathbb{R}^n$ are homotopic via the homotopy $$ f_t(s) = (1-t)f_0(s) + tf_1(s)$$



Am i right in imagining the given homotopy as something like this?



enter image description here



such that $F(s,t) = f_t(s) $ are simply the linesegments going from $f_0(s)$ towards $f_1(s)$ as the straight lines (which "connect" $f_0$ and $f_1$ for every $sin [0,1]$) as drawn in the picture?



Sorry if this question might be a trivial one, i just want to make sure i don't get things wrong.



Thanks for any kind of feedback!






algebraic-topology homotopy-theory path-connected







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    It's correct. Furthermore, any point $s$ moves along its straight line at constant speed.
    $endgroup$
    – Lukas Kofler
    1 hour ago










  • $begingroup$
    isn't the point $t$ rather moving along its straight line? to me, $s$ is the parameter moving along the lines from $x_0$ to $x_1$ whereas $t$ moves along the straight linesegments between $f_0$ and $f_1$
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    That's what I was trying to say, sorry -- a fixed point $f_0(s)$ moves at constant speed as $t$ varies.
    $endgroup$
    – Lukas Kofler
    1 hour ago














1












1








1





$begingroup$


Today i learned about the linear homotopy which says that any two paths $f_0, f_1$ in $mathbb{R}^n$ are homotopic via the homotopy $$ f_t(s) = (1-t)f_0(s) + tf_1(s)$$



Am i right in imagining the given homotopy as something like this?



enter image description here



such that $F(s,t) = f_t(s) $ are simply the linesegments going from $f_0(s)$ towards $f_1(s)$ as the straight lines (which "connect" $f_0$ and $f_1$ for every $sin [0,1]$) as drawn in the picture?



Sorry if this question might be a trivial one, i just want to make sure i don't get things wrong.



Thanks for any kind of feedback!






algebraic-topology homotopy-theory path-connected







share|cite|improve this question









$endgroup$




Today i learned about the linear homotopy which says that any two paths $f_0, f_1$ in $mathbb{R}^n$ are homotopic via the homotopy $$ f_t(s) = (1-t)f_0(s) + tf_1(s)$$



Am i right in imagining the given homotopy as something like this?



enter image description here



such that $F(s,t) = f_t(s) $ are simply the linesegments going from $f_0(s)$ towards $f_1(s)$ as the straight lines (which "connect" $f_0$ and $f_1$ for every $sin [0,1]$) as drawn in the picture?



Sorry if this question might be a trivial one, i just want to make sure i don't get things wrong.



Thanks for any kind of feedback!






algebraic-topology homotopy-theory path-connected




algebraic-topology homotopy-theory path-connected






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 1 hour ago









ZestZest

301213




301213








  • 1




    $begingroup$
    It's correct. Furthermore, any point $s$ moves along its straight line at constant speed.
    $endgroup$
    – Lukas Kofler
    1 hour ago










  • $begingroup$
    isn't the point $t$ rather moving along its straight line? to me, $s$ is the parameter moving along the lines from $x_0$ to $x_1$ whereas $t$ moves along the straight linesegments between $f_0$ and $f_1$
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    That's what I was trying to say, sorry -- a fixed point $f_0(s)$ moves at constant speed as $t$ varies.
    $endgroup$
    – Lukas Kofler
    1 hour ago














  • 1




    $begingroup$
    It's correct. Furthermore, any point $s$ moves along its straight line at constant speed.
    $endgroup$
    – Lukas Kofler
    1 hour ago










  • $begingroup$
    isn't the point $t$ rather moving along its straight line? to me, $s$ is the parameter moving along the lines from $x_0$ to $x_1$ whereas $t$ moves along the straight linesegments between $f_0$ and $f_1$
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    That's what I was trying to say, sorry -- a fixed point $f_0(s)$ moves at constant speed as $t$ varies.
    $endgroup$
    – Lukas Kofler
    1 hour ago








1




1




$begingroup$
It's correct. Furthermore, any point $s$ moves along its straight line at constant speed.
$endgroup$
– Lukas Kofler
1 hour ago




$begingroup$
It's correct. Furthermore, any point $s$ moves along its straight line at constant speed.
$endgroup$
– Lukas Kofler
1 hour ago












$begingroup$
isn't the point $t$ rather moving along its straight line? to me, $s$ is the parameter moving along the lines from $x_0$ to $x_1$ whereas $t$ moves along the straight linesegments between $f_0$ and $f_1$
$endgroup$
– Zest
1 hour ago




$begingroup$
isn't the point $t$ rather moving along its straight line? to me, $s$ is the parameter moving along the lines from $x_0$ to $x_1$ whereas $t$ moves along the straight linesegments between $f_0$ and $f_1$
$endgroup$
– Zest
1 hour ago




1




1




$begingroup$
That's what I was trying to say, sorry -- a fixed point $f_0(s)$ moves at constant speed as $t$ varies.
$endgroup$
– Lukas Kofler
1 hour ago




$begingroup$
That's what I was trying to say, sorry -- a fixed point $f_0(s)$ moves at constant speed as $t$ varies.
$endgroup$
– Lukas Kofler
1 hour ago










2 Answers
2






active

oldest

votes


















2












$begingroup$

Yes. Perhaps to help you see why this is true, pick an arbitrary $s$ value $bar{s}$ and call $a := f_0(bar{s})$ and $b := f_1(bar{s})$. Examining the homotopy,
$$
H_{bar{s}}(t) := F(bar{s}, t) = a(1-t) + bt
$$



we see that it is the parametric equation of a straight line connecting points $a$ and $b$ in $mathbb{R}^n$. If you draw this line for each $bar{s}$ choice, you get your diagram. Perhaps write a bit of code to construct such a plot?



Furthermore, one may be interested in the "speed" at which $a$ "moves" to $b$. We find it to be a constant,
$$
dfrac{dH_{bar{s}}}{dt} = b - a
$$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    this is very helpful @jnez71. Thanks a lot!
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem! I added a bit more to cover some of the comments about speed
    $endgroup$
    – jnez71
    1 hour ago



















1












$begingroup$

Yes, it is absolutely correct.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    thank you very much @Paul. Just being curious, what does it mean that your answer is "community wiki"?
    $endgroup$
    – Zest
    1 hour ago










  • $begingroup$
    See math.stackexchange.com/help/privileges/edit-community-wiki. A community wiki can be edited by everybody. Frankly, my answer was only a feedback, and I guess you didn't expect more. But of course it doesn't deserve positive reputation.
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    thanks Paul. In fact, your answer was all i was hoping for. Would you mind me accepting @jnez72's answer rather than yours even though both helped me?
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem - it is okay!
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    By the way, in my opinion it is important to make it visible in the question queue that a question has been answered. If you click at "Unanswered" in the upper left corne of this page, you will read something like "248,877 questions with no upvoted or accepted answers ", the number of course growing. If you look at these questions, you will see that a great many are actually answered in comments. If that should happen to one of your questions, do not hesitate to write an answer and acknowledge it.
    $endgroup$
    – Paul Frost
    54 mins ago














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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









2












$begingroup$

Yes. Perhaps to help you see why this is true, pick an arbitrary $s$ value $bar{s}$ and call $a := f_0(bar{s})$ and $b := f_1(bar{s})$. Examining the homotopy,
$$
H_{bar{s}}(t) := F(bar{s}, t) = a(1-t) + bt
$$



we see that it is the parametric equation of a straight line connecting points $a$ and $b$ in $mathbb{R}^n$. If you draw this line for each $bar{s}$ choice, you get your diagram. Perhaps write a bit of code to construct such a plot?



Furthermore, one may be interested in the "speed" at which $a$ "moves" to $b$. We find it to be a constant,
$$
dfrac{dH_{bar{s}}}{dt} = b - a
$$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    this is very helpful @jnez71. Thanks a lot!
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem! I added a bit more to cover some of the comments about speed
    $endgroup$
    – jnez71
    1 hour ago
















2












$begingroup$

Yes. Perhaps to help you see why this is true, pick an arbitrary $s$ value $bar{s}$ and call $a := f_0(bar{s})$ and $b := f_1(bar{s})$. Examining the homotopy,
$$
H_{bar{s}}(t) := F(bar{s}, t) = a(1-t) + bt
$$



we see that it is the parametric equation of a straight line connecting points $a$ and $b$ in $mathbb{R}^n$. If you draw this line for each $bar{s}$ choice, you get your diagram. Perhaps write a bit of code to construct such a plot?



Furthermore, one may be interested in the "speed" at which $a$ "moves" to $b$. We find it to be a constant,
$$
dfrac{dH_{bar{s}}}{dt} = b - a
$$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    this is very helpful @jnez71. Thanks a lot!
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem! I added a bit more to cover some of the comments about speed
    $endgroup$
    – jnez71
    1 hour ago














2












2








2





$begingroup$

Yes. Perhaps to help you see why this is true, pick an arbitrary $s$ value $bar{s}$ and call $a := f_0(bar{s})$ and $b := f_1(bar{s})$. Examining the homotopy,
$$
H_{bar{s}}(t) := F(bar{s}, t) = a(1-t) + bt
$$



we see that it is the parametric equation of a straight line connecting points $a$ and $b$ in $mathbb{R}^n$. If you draw this line for each $bar{s}$ choice, you get your diagram. Perhaps write a bit of code to construct such a plot?



Furthermore, one may be interested in the "speed" at which $a$ "moves" to $b$. We find it to be a constant,
$$
dfrac{dH_{bar{s}}}{dt} = b - a
$$






share|cite|improve this answer











$endgroup$



Yes. Perhaps to help you see why this is true, pick an arbitrary $s$ value $bar{s}$ and call $a := f_0(bar{s})$ and $b := f_1(bar{s})$. Examining the homotopy,
$$
H_{bar{s}}(t) := F(bar{s}, t) = a(1-t) + bt
$$



we see that it is the parametric equation of a straight line connecting points $a$ and $b$ in $mathbb{R}^n$. If you draw this line for each $bar{s}$ choice, you get your diagram. Perhaps write a bit of code to construct such a plot?



Furthermore, one may be interested in the "speed" at which $a$ "moves" to $b$. We find it to be a constant,
$$
dfrac{dH_{bar{s}}}{dt} = b - a
$$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 57 mins ago

























answered 1 hour ago









jnez71jnez71

2,495720




2,495720












  • $begingroup$
    this is very helpful @jnez71. Thanks a lot!
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem! I added a bit more to cover some of the comments about speed
    $endgroup$
    – jnez71
    1 hour ago


















  • $begingroup$
    this is very helpful @jnez71. Thanks a lot!
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem! I added a bit more to cover some of the comments about speed
    $endgroup$
    – jnez71
    1 hour ago
















$begingroup$
this is very helpful @jnez71. Thanks a lot!
$endgroup$
– Zest
1 hour ago




$begingroup$
this is very helpful @jnez71. Thanks a lot!
$endgroup$
– Zest
1 hour ago




1




1




$begingroup$
No problem! I added a bit more to cover some of the comments about speed
$endgroup$
– jnez71
1 hour ago




$begingroup$
No problem! I added a bit more to cover some of the comments about speed
$endgroup$
– jnez71
1 hour ago











1












$begingroup$

Yes, it is absolutely correct.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    thank you very much @Paul. Just being curious, what does it mean that your answer is "community wiki"?
    $endgroup$
    – Zest
    1 hour ago










  • $begingroup$
    See math.stackexchange.com/help/privileges/edit-community-wiki. A community wiki can be edited by everybody. Frankly, my answer was only a feedback, and I guess you didn't expect more. But of course it doesn't deserve positive reputation.
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    thanks Paul. In fact, your answer was all i was hoping for. Would you mind me accepting @jnez72's answer rather than yours even though both helped me?
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem - it is okay!
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    By the way, in my opinion it is important to make it visible in the question queue that a question has been answered. If you click at "Unanswered" in the upper left corne of this page, you will read something like "248,877 questions with no upvoted or accepted answers ", the number of course growing. If you look at these questions, you will see that a great many are actually answered in comments. If that should happen to one of your questions, do not hesitate to write an answer and acknowledge it.
    $endgroup$
    – Paul Frost
    54 mins ago


















1












$begingroup$

Yes, it is absolutely correct.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    thank you very much @Paul. Just being curious, what does it mean that your answer is "community wiki"?
    $endgroup$
    – Zest
    1 hour ago










  • $begingroup$
    See math.stackexchange.com/help/privileges/edit-community-wiki. A community wiki can be edited by everybody. Frankly, my answer was only a feedback, and I guess you didn't expect more. But of course it doesn't deserve positive reputation.
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    thanks Paul. In fact, your answer was all i was hoping for. Would you mind me accepting @jnez72's answer rather than yours even though both helped me?
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem - it is okay!
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    By the way, in my opinion it is important to make it visible in the question queue that a question has been answered. If you click at "Unanswered" in the upper left corne of this page, you will read something like "248,877 questions with no upvoted or accepted answers ", the number of course growing. If you look at these questions, you will see that a great many are actually answered in comments. If that should happen to one of your questions, do not hesitate to write an answer and acknowledge it.
    $endgroup$
    – Paul Frost
    54 mins ago
















1












1








1





$begingroup$

Yes, it is absolutely correct.






share|cite|improve this answer











$endgroup$



Yes, it is absolutely correct.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








answered 1 hour ago


























community wiki





Paul Frost













  • $begingroup$
    thank you very much @Paul. Just being curious, what does it mean that your answer is "community wiki"?
    $endgroup$
    – Zest
    1 hour ago










  • $begingroup$
    See math.stackexchange.com/help/privileges/edit-community-wiki. A community wiki can be edited by everybody. Frankly, my answer was only a feedback, and I guess you didn't expect more. But of course it doesn't deserve positive reputation.
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    thanks Paul. In fact, your answer was all i was hoping for. Would you mind me accepting @jnez72's answer rather than yours even though both helped me?
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem - it is okay!
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    By the way, in my opinion it is important to make it visible in the question queue that a question has been answered. If you click at "Unanswered" in the upper left corne of this page, you will read something like "248,877 questions with no upvoted or accepted answers ", the number of course growing. If you look at these questions, you will see that a great many are actually answered in comments. If that should happen to one of your questions, do not hesitate to write an answer and acknowledge it.
    $endgroup$
    – Paul Frost
    54 mins ago




















  • $begingroup$
    thank you very much @Paul. Just being curious, what does it mean that your answer is "community wiki"?
    $endgroup$
    – Zest
    1 hour ago










  • $begingroup$
    See math.stackexchange.com/help/privileges/edit-community-wiki. A community wiki can be edited by everybody. Frankly, my answer was only a feedback, and I guess you didn't expect more. But of course it doesn't deserve positive reputation.
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    thanks Paul. In fact, your answer was all i was hoping for. Would you mind me accepting @jnez72's answer rather than yours even though both helped me?
    $endgroup$
    – Zest
    1 hour ago






  • 1




    $begingroup$
    No problem - it is okay!
    $endgroup$
    – Paul Frost
    1 hour ago










  • $begingroup$
    By the way, in my opinion it is important to make it visible in the question queue that a question has been answered. If you click at "Unanswered" in the upper left corne of this page, you will read something like "248,877 questions with no upvoted or accepted answers ", the number of course growing. If you look at these questions, you will see that a great many are actually answered in comments. If that should happen to one of your questions, do not hesitate to write an answer and acknowledge it.
    $endgroup$
    – Paul Frost
    54 mins ago


















$begingroup$
thank you very much @Paul. Just being curious, what does it mean that your answer is "community wiki"?
$endgroup$
– Zest
1 hour ago




$begingroup$
thank you very much @Paul. Just being curious, what does it mean that your answer is "community wiki"?
$endgroup$
– Zest
1 hour ago












$begingroup$
See math.stackexchange.com/help/privileges/edit-community-wiki. A community wiki can be edited by everybody. Frankly, my answer was only a feedback, and I guess you didn't expect more. But of course it doesn't deserve positive reputation.
$endgroup$
– Paul Frost
1 hour ago




$begingroup$
See math.stackexchange.com/help/privileges/edit-community-wiki. A community wiki can be edited by everybody. Frankly, my answer was only a feedback, and I guess you didn't expect more. But of course it doesn't deserve positive reputation.
$endgroup$
– Paul Frost
1 hour ago












$begingroup$
thanks Paul. In fact, your answer was all i was hoping for. Would you mind me accepting @jnez72's answer rather than yours even though both helped me?
$endgroup$
– Zest
1 hour ago




$begingroup$
thanks Paul. In fact, your answer was all i was hoping for. Would you mind me accepting @jnez72's answer rather than yours even though both helped me?
$endgroup$
– Zest
1 hour ago




1




1




$begingroup$
No problem - it is okay!
$endgroup$
– Paul Frost
1 hour ago




$begingroup$
No problem - it is okay!
$endgroup$
– Paul Frost
1 hour ago












$begingroup$
By the way, in my opinion it is important to make it visible in the question queue that a question has been answered. If you click at "Unanswered" in the upper left corne of this page, you will read something like "248,877 questions with no upvoted or accepted answers ", the number of course growing. If you look at these questions, you will see that a great many are actually answered in comments. If that should happen to one of your questions, do not hesitate to write an answer and acknowledge it.
$endgroup$
– Paul Frost
54 mins ago






$begingroup$
By the way, in my opinion it is important to make it visible in the question queue that a question has been answered. If you click at "Unanswered" in the upper left corne of this page, you will read something like "248,877 questions with no upvoted or accepted answers ", the number of course growing. If you look at these questions, you will see that a great many are actually answered in comments. If that should happen to one of your questions, do not hesitate to write an answer and acknowledge it.
$endgroup$
– Paul Frost
54 mins ago




















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Olav Thon

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Olav Thon Fødd 29. juni 1923 Ål Yrke forretningsdrivande Olav Thon på Commons Olav Thon (fødd 29. juni 1923) er ein norsk, stort sett sjølvlært forretningsmann, fødd i Ål i Hallingdal, som har gjort store pengar på særleg kjøp, bygging og utvikling av fast eigedom, mellom anna kjøpesentre, hotell og restaurantar, i både Noreg og somme andre land. Han vart Ridder av 1. klasse av St. Olavs Orden i 2003, og er som ivrig friluftsmann æresmedlem i Den Norske Turistforening etter å ha ytt store økonomiske bidrag til foreininga sine hytter og ruter i fjellet. Han er kjend for alltid å gå med ei karakteristisk strikkelue. Olav Thon i samtale med Trond Helleland på sentralbanksjefens årstale i februar 2016 I ung alder reiste Olav Thon til Newcastle for å lære seg engelsk, og han var seinare ei tid i Sveits, der han gjorde forretningar i import og eksport. Deretter tok han til å kjøpe faste eigedomar i Noreg med stor økonomisk suksess, verksemda voks snøgt og v
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Waikiki

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Denne artikkelen kan ha godt av ein språkvask , som reinskar opp målføringa og/eller innfører same språkstilen overalt. Denne artikkelen kan ha godt av ei opprydding for å nå ein høgare standard og/eller for å verta i tråd med standardoppsettet. Sjå korleis du redigerer ei side og stilmanualen for hjelp. Waikiki Land   USA Stat Hawaii Stad Honolulu Wikimedia Commons: Waikiki Utsyn over Waikiki Waikīkī er ein bydel i Honolulu, sør på øya Oahu, som er ei av Hawaii-øyane. Waikīkīstranda er ein av dei meste berømte strendene i verda. Waikīkī strekkjer seg langs stillehavskysten og har ei rekkje velrenommerte hotell. Bydelen er Hawaii-turismens høyborg. På Waikīkī Beach står ei statue av den lokale sportsstjerna Duka Kahanamoku. Kjelder | Denne artikkelen bygger på «Waikiki» frå Wikipedia på bokmål, den 4. november 2018. Denne artikkelen manglar kjelder eller referansar . Hjelp Wikipedia med å finna truverdige kjelder
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Hudsonelva

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Hudson elv Land   USA Område New York Sideelvar Mohawk Lengd 507 km Middelvassføring 606 m³/s Munning Upper New York Bay i Atlanterhavet Elvene Hudson og Mohawk med nedbørsområdet markert med gult. Wikimedia Commons: Hudson River Hudsonelva ( Hudson River ) mohikansk Muh-he-kun-ne-tuk ) er ei elv i USA. Ho renn hovudsakleg gjennom delstaten New York, men markerer også ein del av grensa mellom New York og New Jersey. Hudsonelva har namn etter Henry Hudson, ein engelskmann som utforska elva i 1609. Hudsonelva sett frå Bear Mountain Bridge. Kjelda til elva er Tear-of-the-Clouds-sjøen i Adirondackfjella. Ved Albany renn Mohawk-elva saman med henne, og deretter renn ho nesten rett sørover til ho munnar ut i Atlanterhavet mellom Manhattan i New York og New Jersey. Eriekanalen, som blei opna den 26 oktober 1825, bind saman Hudsonelva og Eriesjøen, slik at byane ved Dei store sjøane fekk vasstilgang til A
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