Let p: (0,10) --> S^1, p(t) = (cos t, sin t).
Show that p is a local homomorphism, but ((0,10), p) is NOT a covering space of S^1.
For x in (0,10) find open U nhood x small
enuf so that f(U) doesn't wrap around ...
Covering space of S^1 and Homomorphisms are investigated and discussed in the solution.
Covering Spaces : Compact Hausdorff Spaces and Homomorphisms
Assume X and Y are arcwise connected and locally arcwise connected, X is compact Hausdorff, and Y is Hausdorff. Let f: X-->Y be a local homeomorphism. Prove that (X,f) is a covering space.View Full Posting Details