Fixed-point property: Difference between revisions
m (Fixed point property moved to Fixed-point property) |
No edit summary |
||
| Line 4: | Line 4: | ||
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. | 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 space|acyclic]] [[compact space|compact]] [[polyhedron]] (nonempty) | |||
==Facts== | ==Facts== | ||
| Line 9: | Line 15: | ||
* [[Lefschetz fixed-point theorem]] | * [[Lefschetz fixed-point theorem]] | ||
* [[Brouwer fixed-point theorem]] | * [[Brouwer fixed-point theorem]] | ||
* Every retract of a space with the fixed-point property also has the fixed-point property | |||
Revision as of 22:44, 27 October 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
- Lefschetz fixed-point theorem
- Brouwer fixed-point theorem
- Every retract of a space with the fixed-point property also has the fixed-point property