# Local homeomorphism and coverings

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?

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