# Pairings and Copairings in the Category of Topological Spaces

### Nobuyuki Oda

Fukuoka University, Japan

## Abstract

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 Sugawara 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 Hilton, Mislin and Roitberg.

## Cite this article

Nobuyuki Oda, Pairings and Copairings in the Category of Topological Spaces. Publ. Res. Inst. Math. Sci. 28 (1992), no. 1, pp. 83–97

DOI 10.2977/PRIMS/1195168857