If a space X is arcwise connected, then for any two points p and q in X the fundamental groups ##\pi_1(X,p)## and ##\pi_1(X,q)## are isomorphic. This means that we can, up to isomorphisms, identify both groups with their equivalence class ##\pi_1(X)##.(adsbygoogle = window.adsbygoogle || []).push({});

I started to think about the generality of this theorem. Is there any interesting/important spaces which are not arcwise connected except for the union of two disjoint spaces etc?

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# Fundamental groups and arcwise connected spaces.

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