High Quality Content by WIKIPEDIA articles! In mathematics, particularly topology, a perfect map is a particular kind of continuous function between topological spaces. Perfect maps are weaker than homeomorphisms, but strong enough to preserve some topological properties such a local compactness that are not always preserved by continuous maps. Let X and Y be topological spaces and let p be a map from X to Y that is continuous, closed, surjective and such that p ?1(y) is compact relative to X for each y in Y. Then p is known as a perfect map.

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