Homotopy equivalence of topological spaces

From Topospaces

Definition

Suppose and are topological spaces. A homotopy equivalence between and is a map such that there exists a map for which is homotopic to the identity on and is homotopic to the identity on .

Two topological spaces between which there exists a homotopy equivalence are termed homotopy-equivalent topological spaces.

Relation with other properties

Stronger properties

Weaker properties

Related notions