Absolute retract

From Topospaces

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 termed an absolute retract if it satisfies the following equivalent conditions:

  • Whenever it is embedded as a closed subspace of a normal space, it is a retract of that topological space
  • Given any normal space and a closed subspace, any map from the closed subspace to this space, extends to a map from the whole normal space to this space.

Relation with other properties

Weaker properties