Explore BrainMass

# Covering Spaces : Compact Hausdorff Spaces and Homomorphisms

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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.

https://brainmass.com/math/geometry-and-topology/covering-spaces-compact-hausdorff-spaces-homomorphisms-72501

#### Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Covering Spaces: Algebraic Topology problem
________________________________________
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.

Solution:

an arc connecting two points and of a topological space is not simply (like a path) a continuous function such that and , but must also have a continuous inverse function, i.e., that it is a homeomorphism between and the image of f.

If s is compact subspace in a ...

#### Solution Summary

Covering Spaces, Compact Hausdorff Spaces and Homomorphisms are investigated. The solution is detailed and well presented.

\$2.49