Fixed-point property

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

Metaproperties

Every retract of a space with the fixed-point property also has the fixed-point property