• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1589-1600
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• 2019

In this paper, we apply the notion of cocyclic maps to the category of pairs proposed by Hilton and obtain more general concepts. We discuss the concept of cocyclic morphisms with respect to a morphism and find that it is a dual concept of cyclic morphisms with respect to a morphism and a generalization of the notion of cocyclic morphisms with respect to a map. Moreover, we investigate its basic properties including the preservation of cocyclic properties by morphisms and find conditions for which the set of all homotopy classes of cocyclic morphisms with respect to a morphism will have a group structure.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.61-71
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• 2003

We obtain a necessary condition for splitting T-space off a space in terms of cyclic maps, and also obtain a necessary condition for splitting co-T-spaces in terms of cocyclic maps.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.39-47
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• 2009

Pan, Shen and Woo [8] introduced the concept of the G-sequence of a map. We introduce the G'-sequence of a map, which is a dual concept of the G-sequence of a map. We obtain some sufficient conditions for the all sets in the G'-sequence of a map are groups, and for the exact G'-sequence of a map.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1623-1639
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• 2017

The generalized coGottlieb sets are not known to be groups in general. We study some conditions which make them groups. Moreover, there are actions on the generalized coGottlieb sets which are different from known actions up to now. We give related exact sequence of the generalized coGottlieb sets. Using them, we obtain certain results related to the maps which preserve generalized coGottlieb sets.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.101-113
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• 2005

We define and study a concept of $T_A$-space which is closely related to the generalized Gottlieb group. We know that X is a $T_A$-space if and only if there is a map $r:L(A,\;X){\rightarrow}L_0(A,\;X)$ called a $T_A$-structure such that $ri{\sim}1_{L_0(A,\;X)}$. The concepts of $T_{{\Sigma}B}$-spaces are preserved by retraction and product. We also introduce and study a dual concept of $T_A$-space.