Absolute neighbourhood retract

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 $X$ is termed an absolute neighbourhood retract or ANR if whenever $X$ is embedded as a closed subset of some topological space $Y$, then there exists an open set $U$ containing $X$ such that $X$ is a retract of $U$.

Relation with other properties

Stronger properties

• Absolute retract