Perfect map: Difference between revisions
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==Definition== | ==Definition== | ||
A [[continuous map]] between [[topological space]]s is termed a '''perfect map''' if the inverse image of any point in the image space, is a [[compact space|compact subset]] of the domain space. | A [[continuous map]] between [[topological space]]s is termed a '''perfect map''' if it is a surjective, [[closed map|closed]] and the inverse image of any point in the image space, is a [[compact space|compact subset]] of the domain space. | ||
==Relation with other properties== | ==Relation with other properties== | ||
=== | ===Related properties=== | ||
* [[Proper map]] | * [[Proper map]] | ||
Revision as of 01:29, 27 October 2007
This article defines a property of continuous maps between topological spaces
Definition
A continuous map between topological spaces is termed a perfect map if it is a surjective, closed and the inverse image of any point in the image space, is a compact subset of the domain space.