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Perfect map 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. ==Formal definition==
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.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Perfect map」の詳細全文を読む
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