Fixed-point property: Difference between revisions
No edit summary |
No edit summary |
||
| Line 15: | Line 15: | ||
* [[Lefschetz fixed-point theorem]] | * [[Lefschetz fixed-point theorem]] | ||
* [[Brouwer fixed-point theorem]] | * [[Brouwer fixed-point theorem]] | ||
==Metaproperties== | |||
{{retract-closed}} | |||
Every retract of a space with the fixed-point property also has the fixed-point property | |||
Revision as of 01:25, 3 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
A topological space is said to have the fixed-point property if every continuous map from the topological space to itself, has a fixed point.
Relation with other properties
Stronger properties
- acyclic compact polyhedron (nonempty)
Facts
Metaproperties
Every retract of a space with the fixed-point property also has the fixed-point property