At the end of cheapter $8.1$,  $4)$ Given spaces $X$ and $Y$, let $[X,Y]$ denote the set of homotopy classes of maps of $X$ into $Y$.  $b)$ Show that if $Y$ is path connected, the set $[I,Y]$ has a single element.($I=[0,1]$)    Claim$1:$  If $Y$ contains a hole then the loop containing the hole can not be homotopic to the ones which is not containing. So is it wrong ?    Claim$2:$  Beside that, when I first try to prove the claim,  Let $f:I\to Y$ be a continious map. Set $$F:I\times I\to Y$$  $$(x,t)\mapsto f(x(1-t)) $$  Then $f$ is homotopic to a constant map. As $Y$ is path connected all constant map is homotopic to each other. Thus we are done.    But I am not sure about niether of them.
So I came across this exercise: Show that if $Y$ is path-connected then the set of homotopy classes $[I,Y]$ of maps of $I=[0,1]$ into Y has a single point.   But I am confused here. If $Y=S^1$ then not all loops are homotopic! I mean, isn't true that $\pi_1(Y)\subset [I,Y]$? Or maybe I don't understand the set $[I,Y]$ well!
I saw this bug mentioned in image below, where in I was about to mark the question as duplicate..    Has you can see there is no radio buttons to select and go further.. And I am stuck..  Is this a KNOWN bug..  I am using Mozilla Firefox Browser..  Edit:-  As guided by @AzizShaikh, This kind of behaviour is observed when you have already flagged a post. In my opinion, I think the page as I mentioned above should not have come in first place, I mean don't allow the user to enter it doesn't belong here, or it is a duplicate section if his vote has been posted successfully for that section rather than showing go nowhere Im lost Screen ..  Can we do something about this...?? , clicking &quot;link&quot; &quot;share&quot; for anwers yields a short (traceable) URL in the &quot;share a link to this answer&quot; dialog, such as †:  These short URLs show no clue about the linked question whatsoever. Also, when different people use a short URL for the very same post, then the user id suffix makes those be different URLs for a browser. Such links will then not be shown as visited‡. I know how to get URLs that have a proper slug. But as I see  pop up on these sites (where referrals ), I assume many others just don't realize full URLs would be better for use on these sites themselves? Or many don't want to do the little effort to get the full URL? So: can we please have an easy way to get the full URL as well, in a way that is easily found for those who don't know about the different links? (Currently for questions, clicking &quot;link&quot; has the same effect. But then one can also right-click the title, or take the URL from the location bar, to get the full human-readable URL. Once, Jeff .)  † The short links for answers are not (yet) [automatically converted][6] into a clickable question title either, unlike links such as `https://meta.stackexchange.com/questions/74274/privacy-leak-in-permalink#75963`, which renders as https://meta.stackexchange.com/questions/74274/privacy-leak-in-permalink#75963 But I guess that will change soon.  ‡ On Meta the CSS for posts doesn't indicate such difference anyway, which is a different issue. How to change color for a block of texts? How do I run two isolated instances of firefox? For example block cipher AES-128, Key size is 128bit and it is used to make a 10 round key which is total 320bit.  Question 1. If i use another Key schedule algorithm in AES, then security decreased or remain same? In other words, if the key schedule algorithm of AES has some relationship with AES encryption itself, then it will be decreased, or it will be same if the new key schedule algorithm is safe enough.  Question 2. 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