- #1
center o bass
- 560
- 2
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)##.
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?
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?