H-space

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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.