This is a question regarding lack of formation of Fundamental Group, could any one give an easy example why the product of two path homotopy class is not defined in a space $X$? Thank you.
2026-04-03 19:43:58.1775245438
why product of two path homotopy class is not always defined?
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If two paths have the same start and end points, then they can be concatenated to produce another path with the same start and end point. That's the same sort of thing you started with, which should give you hope that perhaps you can build an algebraic object out of paths starting and ending at the same point. However, you have no such luck with two random paths.