Supercompact space: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Compact metrizable space]] | * [[Compact metrizable space]] | ||
* [[Compact linearly orderable space]] | * [[Compact linearly orderable space]] | ||
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===Weaker properties=== | ===Weaker properties=== | ||
* [[Compact space]]: {{proofat|[[Alexander subbase | * [[Compact space]]: {{proofat|[[Alexander subbase theorem]]}} | ||
==Metaproperties== | ==Metaproperties== | ||
Latest revision as of 18:33, 28 January 2012
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 supercompact if it has a subbasis such that any open cover of the topological space whose elements come from the subbasis, has a subcover comprising at most two members.
Relation with other properties
Stronger properties
Weaker properties
- Compact space: For full proof, refer: Alexander subbase theorem
Metaproperties
Products
This property of topological spaces is closed under taking arbitrary products
View all properties of topological spaces closed under products
An arbitrary product of supercompact spaces is supercompact, in the product topology.