Regular Lindelof space: Difference between revisions

Revision as of 20:31, 15 December 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

Symbol-free definition

A topological space is termed regular Lindelof if it is regular and Lindelof.

Relation with other properties

Stronger properties

Metrizable space

Weaker properties

Paracompact Hausdorff space

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 ===Symbol-free definition===
-A [[topological space]] is termed '''regular Lindelof''' if it satisfies the following equivalent conditions:
+A [[topological space]] is termed '''regular Lindelof''' if it is [[regular space|regular]] and [[Lindelof space|Lindelof]].
-* It is [[regular space|regular]] and [[Lindelof space|Lindelof]]: every open cover has a [[locally finite collection of subsets|locally finite]] open [[refinement]]
-* It is [[regular space|regular]] and every open cover has a locally finite closed refinement
-* It is [[regular space|regular]] and every open cover has a locally finite refinement
-* It is [[regular space|regular]] and every open cover has a [[countable locally finite collection of subsets|countably locally finite]] open refinement
 ==Relation with other properties==