H-space

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 based topological space $(X,x_{0})$ is termed a H-space if there is a map of pointed spaces $m:(X,x_{0})\times (X,x_{0})\to (X,x_{0})$ such that each of the maps $m(x_{0},\ )$ and $m(\ ,x_{0})$ is homotopic to the identity at $X$ at $x_{0}$. The point $x_{0}$ is termed a homotopy identity.