Hopf space

An H-space, named after Heinz Hopf, and sometimes also called a Hopf space, is a topological space together with a continuous binary operation μ:X×X->X, such that there exists a point e element X with the property that the two maps x↦μ(x, e) and x↦μ(e, x) are both homotopic to the identity map id_X on X, through homotopies preserving the point e. The element e is called a homotopy identity.

co-H-space | fundamental group | Hopf invariant one theorem