Weak homotopy equivalence of topological spaces

This article defines a property that can be evaluated for a map between topological spaces. Note that the map is not assumed to be continuous

Definition

Let $A$ and $B$ be topological spaces. A weak homotopy equivalence from $A$ to $B$ is a continuous map $f:A\to B$ such that the functorially induced maps $\pi _{n}(f):\pi _{n}(A)\to \pi _{n}(B)$ are isomorphisms for all $n$.

Relation with other properties

Stronger properties

• Homotopy equivalence of topological spaces
• Chain complex-equivalence of topological spaces