Feebly compact space: Difference between revisions
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==Definition== | ==Definition== | ||
A [[topological space]] is termed '''feebly compact''' if every [[locally finite collection]] of nonempty [[open subset]]s is finite. | A [[topological space]] is termed '''feebly compact''' or '''lightly compact''' if every [[locally finite collection]] of nonempty [[open subset]]s is finite. | ||
==Relation with other properties== | ==Relation with other properties== | ||
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* [[Compact space]]: {{proofat|[[Compact implies feebly compact]]}} | * [[Compact space]]: {{proofat|[[Compact implies feebly compact]]}} | ||
===Weaker properties=== | |||
* [[Pseudocompact space]] | |||
Revision as of 13:22, 18 August 2007
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This is a variation of compactness. View other variations of compactness
Definition
A topological space is termed feebly compact or lightly compact if every locally finite collection of nonempty open subsets is finite.
Relation with other properties
Stronger properties
- Compact space: For full proof, refer: Compact implies feebly compact