Pairings and copairings in the category of topological spaces
type: Item
instance of: scholarly article
title: Pairings and copairings in the category of topological spaces
zbMATH Open document ID: 0797.55008
author: Nobuyuki Oda
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1994-10-19T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 55P91
zbMATH DE Number: 548923
zbMATH Keywords: pairings
zbMATH Keywords: homotopy sets
zbMATH Keywords: copairings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195168857
OpenAlex ID: W2073289115
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DOI: 10.2977/PRIMS/1195168857
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description: scientific article; zbMATH DE number 548923