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
Metaproperties
Retract-hereditariness
This property of topological spaces is hereditary on retracts, viz if a space has the property, so does any retract of it
View all retract-hereditary properties of topological spaces
Every retract of a space with the fixed-point property also has the fixed-point property