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.
Jiyean Kim and Kee Young Lee
Korea University, Korea University
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
2019; 56(6): 1589-1600
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