Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'd like to prove that if $p : Y \to X$ is a covering projection, then $Y$ is locally path-connected if $ X$ is.

I've tried a load of different things, but can't get it to work. Any hints / references to proofs online (I haven't been able to find any) would be greatly appreciated. Thanks

share|improve this question
2  
What is the problem? By hypothesis you have a base of path connected sets around every point in $X$ and $p$ is a local homeomorphism. –  t.b. Nov 2 '11 at 18:18
2  
Hint: you want to prove something about small neighborhoods in Y and you're given information about some neighborhoods in X. Being a covering projection says something about small enough neighborhoods in Y actually being homeomorphic to neighborhoods in X; just figure out how the quantifiers go and you're done. –  Omar Antolín-Camarena Nov 2 '11 at 18:20

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.