Proper map: Difference between revisions
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{{ | {{continuous map property}} | ||
==Definition== | ==Definition== | ||
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if it is [[closed map|closed]] the inverse image of any [[compact space|compact subset]] in the image set, is a compact subset of the domain. | A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if it is [[closed map|closed]] and the inverse image of any [[compact space|compact subset]] in the image set, is a compact subset of the domain. Equivalently, it is a [[closed map]] and the inverse image of any point is a compact subset of the domain. | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Perfect map]] | |||
===Related properties=== | |||
* [[Separated map]] | |||
Latest revision as of 19:57, 11 May 2008
This article defines a property of continuous maps between topological spaces
Definition
Symbol-free definition
A continuous map of topological spaces is termed a proper map if it is closed and the inverse image of any compact subset in the image set, is a compact subset of the domain. Equivalently, it is a closed map and the inverse image of any point is a compact subset of the domain.