# Difference between revisions of "Absolute retract for normal spaces"

A topological space $X$ such that every mapping $g\colon A\to X$ of any closed subset $A$ of an arbitrary normal space $Y$ can be extended to the entire space $Y$. A direct product of absolute retracts for normal spaces is an absolute retract for normal spaces, as is any retract (cf. Retract of a topological space) of an absolute retract for normal spaces. In particular, the following spaces are absolute retracts for normal spaces: the unit interval $I$; the $n$-dimensional cube $I^n$; and the Hilbert cube $I^\omega$. Any two mappings of a binormal space into an absolute retract for normal spaces are homotopic; while a binormal absolute retract for normal spaces is contractible into a point.

A binormal space is a space $X$ for which the product $X\times I$ is normal. It can be proved that a space $X$ is binormal if and only if $X$ is normal and countably paracompact (cf. Paracompactness criteria).