Pairings and copairings in the category of topological spaces
Pairings and copairings in the category of topological spaces
复制标题
拓扑空间范畴中的配对和共配对
DOI：
10.2977/prims/1195168857
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发表时间：
1992
影响因子：
1.2
通讯作者：
Nobuyuki Oda
中科院分区：
文献类型：
--
作者：
Nobuyuki Oda
证明了一个定理，该定理给出了拓扑空间的对与同伦集的对之间的关系。作为该定理的直接结果，我们得到了关于同伦集合元素交换性的许多结果。作为该定理的进一步应用，我们证明了当目标空间为Hopf空间时，关于同伦集合中逆元素存在性的Sugawara定理的推广。我们还证明了对偶结果，它是Hilton， Mislin和Roitberg定理的推广。
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.