In mathematics, especially 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 as local compactness that are not always preserved by continuous maps.
Let and be topological spaces and let be a map from to that is continuous, closed, surjective and such that each fiber is compact relative to for each in . Then is known as a perfect map.