Fixed-point property: Difference between revisions
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Every retract of a space with the fixed-point property also has the fixed-point property | 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
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