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.