##### Wikipedia

**H-space**

In mathematics, an **H-space**, or a **topological unital magma**, is a topological space*X* (generally assumed to be connected) together with a continuous map μ : *X* × *X* → *X* with an identity element*e* so that μ(*e*, *x*) = μ(*x*, *e*) = *x* for all *x* in *X*. Alternatively, the maps μ(*e*, *x*) and μ(*x*, *e*) are sometimes only required to be homotopic to the identity (in this case *e* is called homotopy identity), sometimes through basepoint preserving maps. These three definitions are in fact equivalent for H-spaces that are CW complexes. Every topological group is an H-space; however, in the general case, as compared to a topological group, H-spaces may lack associativity and inverses.