local homeomorphism

A surjective mapping $f: X \to Y$ between compact spaces is said to be (see [59, Chapter 3 and 4, p. 12-28]):
- a local homeomorphism provided that for each point $x \in X$ there exists a an open neighborhood U of x such that f(U) is an open neighborhood of f(x) and that f restricted to U is a homeomorphism between U and f(U).