Local homeomorphism

In mathematics, more specifically topology, a local homeomorphism is a function between topological spaces that, intuitively, preserves local (though not necessarily global) structure.

Let X and Y be topological spaces. A function ${\displaystyle f:X\to Y\,}$ is a local homeomorphism if for every point x in X there exists an open set U containing x, such that the image ${\displaystyle f(U)}$ is open in Y and the restriction ${\displaystyle f|_{U}:U\to f(U)\,}$ is a homeomorphism.

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