Lindelof space: Difference between revisions
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The product of two Lindelof spaces need not be a Lindelof space. | The product of two Lindelof spaces need not be a Lindelof space. A counterexample is the [[Sorgenfrey plane]], which is a product of two copies of the [[Sorgenfrey line]]. | ||
==References== | |||
===Textbook references=== | |||
* {{booklink|Munkres}}, Page 192 (definition in paragraph) | |||
Latest revision as of 19:48, 11 May 2008
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 said to be Lindelof if every open cover of it has a countable subcover.
Relation with other properties
Stronger properties
Weaker properties
Metaproperties
The product of two Lindelof spaces need not be a Lindelof space. A counterexample is the Sorgenfrey plane, which is a product of two copies of the Sorgenfrey line.
References
Textbook references
- Topology (2nd edition) by James R. MunkresMore info, Page 192 (definition in paragraph)