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GOTTLIEB SUBSETS WITH RESPECT TO A MORPHISM IN THE CATEGORY OF PAIRS

Authors
Kim, JiyeanLee, Kee Young
Issue Date
Nov-2010
Publisher
KOREAN MATHEMATICAL SOC
Keywords
category of pairs; cyclic map; cyclic morphism; generalized Gottlieb subset
Citation
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.47, no.6, pp.1311 - 1327
Indexed
SCIE
SCOPUS
KCI
Journal Title
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
Volume
47
Number
6
Start Page
1311
End Page
1327
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/115402
DOI
10.4134/BKMS.2010.47.6.1311
ISSN
1015-8634
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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