Pairings and copairings in the category of topological spaces
Summary: We prove a theorem which gives a relation between the pairings of homotopy sets induced by pairings and copairings of topological spaces. We obtain many results on commutativity of elements of homotopy sets as immediate consequences of the theorem. As a further application of the theorem, we prove a generalization of a theorem of \textit{M. Sugawara} [Math. J. Okayama Univ. 6, 109-129 (1957; Zbl 0077.167); 7, 123-149 (1957; Zbl 0091.372)] on the existence of inverse element in the homotopy set when the target space is a Hopf space. We also prove the dual result which is a generalization of a theorem of \textit{P. Hilton, G. Mislin} and \textit{J. Roitberg} [Comment. Math. Helv. 53, 1-14 (1978; Zbl 0372.55009)].
scientific article; zbMATH DE number 548923
scientific article