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.

Let $f: X \rightarrow Y$ be a local homeomorphism with X, Y connected, locally path connected, Hausdorff and with X also compact. Then f is also a covering with finite fibers.

I know how to show that the fibers are finite. Given that f is a surjection, I know how to show that f is a covering map.

How do I show that f is surjective?

share|improve this question

1 Answer 1

up vote 5 down vote accepted

I think I have it. The image of X under f is open (use "local homeomorphism") and closed (use "compact" and "Hausdorff") in Y and since Y is connected this shows that the image is the whole of Y.

share|improve this answer

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.