Certain Generalizations of G-Sequences and Their Exactness

Lee, Kee Young; Woo, Moo Ha; Zhao, Xuezhi

doi:10.4134/bkms.2008.45.1.119

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2010

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“…He studied the role of cyclic maps and cocyclic maps in the set up of Eckmann-Hilton duality. In [6,8], Lee and Woo introduced the concept of the G-sequence under the homotopy sequence and its generalization. Moreover, they introduced the concept of cyclic morphisms with respect to a continuous map as a generalization of the concept of cyclic maps in [7].…”

Section: Introductionmentioning

confidence: 99%

Gottlieb Subsets With Respect to a Morphism in the Category of Pairs

Kim¹,

Lee²

2010

Bulletin of the Korean Mathematical Society

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Abstract. We introduce the concept of cyclic morphisms with respect to a morphism in the category of pairs as a generalization of the concept of cyclic maps and we use the concept to obtain certain sets of homotopy classes in the category of pairs. For these sets, we get complete or partial answers to the following questions: (1) Is the concept the most general concept in the class of all concepts of generalized Gottlieb subsets introduced by many authors until now? (2) Are they homotopy invariants in the category of pairs? (3) When do they have a group structure?

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Section: Introductionmentioning

confidence: 99%