Homotopy associativity of 𝐻-spaces. I

JAMES DILLON STASHEFF(i) 1. Introduction. The concept of an //-space arose as a generalization of that of a topological group. The essential feature which is retained is a continuous multiplication with a unit. There is a significant class of spaces which are //-spaces but not topological groups. Some of the techniques which apply to topological groups can be applied to //-spaces, but not all. From the point of view of homotopy theory, it is not the existence of a continuous inverse which is the important distinguishing feature 6; 15, but rather the associativity of the multiplication.