Talk:Homotopy
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I think it is not true as stated in the article, that when X and Y are homotopy equivalent, and X is locally path connected, then Y is also locally path connected. For an example, take the subspace of a unit square consisting of the interval [(0,0),(0,1)] together with all line segments from (0,1) to the points (1/n,0) where n runs through all natural numbers. The space is contractible, but it is not locally path connected at (0,0).
I am not sure that the statement that two homotopies can be rotated makes much sense (but I know what is meant..:) )
Yes, locally path-connected isn't a homotopy invariant.
It seems to me the stuff on homotopy groups belongs in its own article. --gorlim 16:52, 24 Apr 2004 (UTC)