Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(6): 1311-1327

Printed November 1, 2010

https://doi.org/10.4134/BKMS.2010.47.6.1311

Copyright © The Korean Mathematical Society.

Gottlieb subsets with respect to a morphism in the category of pairs

Jiyean Kim and Kee Young Lee

Korea University, Korea University

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?

Keywords: category of pairs, cyclic map, cyclic morphism, generalized Gottlieb subset

MSC numbers: Primary 55Q05; Secondary 55P30

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