P-space: Difference between revisions
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A topological space is termed a '''P-space''' if every <math>G_\delta</math>-[[G-delta subset|subset]] in it is open. | A topological space is termed a '''P-space''' if every <math>G_\delta</math>-[[G-delta subset|subset]] in it is open. | ||
==Formalisms== | |||
{{subspace property implication}} | |||
The property of being a P-space can be described as the following implication between properties of subsets: | |||
<math>G_\delta \implies</math> Open | |||
==Relation with other properties== | ==Relation with other properties== | ||
===Stronger properties=== | |||
* [[Alexandroff space]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[P'-space]] | * [[P'-space]] | ||
* [[Countably orthocompact space]] | |||
Revision as of 12:58, 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
Definition
A topological space is termed a P-space if every -subset in it is open.
Formalisms
Subspace property implication formalism
This property of topological spaces can be encoded by the fact that one subspace property implies another
The property of being a P-space can be described as the following implication between properties of subsets:
Open