Absolute retract: Difference between revisions
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==Definition== | ==Definition== | ||
A [[topological space]] is termed an '''absolute retract''' if | A [[topological space]] is termed an '''absolute retract''' if it satisfies the following equivalent conditions: | ||
* Whenever it is embedded as a closed subspace of a [[normal space]], it is a [[retract]] of that topological space | |||
* Given any [[normal space]] and a closed subspace, any map from the closed subspace to this space, extends to a map from the whole normal space to this space. | |||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 23:44, 10 November 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 an absolute retract if it satisfies the following equivalent conditions:
- Whenever it is embedded as a closed subspace of a normal space, it is a retract of that topological space
- Given any normal space and a closed subspace, any map from the closed subspace to this space, extends to a map from the whole normal space to this space.