H-space

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.