• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.47-56
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• 2014

In this paper, we introduce and study the concepts of weak $C^f_k$-spaces for maps which are generalized concepts of $C^f_k$-spaces for maps, and introduce the dual concepts of weak $C^f_k$-spaces for maps and obtain some dual results.

• 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.

• 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.24 no.1
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• pp.137-140
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• 2011

It is known [5] that the concepts of $C_k$-spaces and those can be characterized using by the Gottlieb sets and the LS category of spaces as follows; A space X is a $C_k$-space if and only if the Gottlieb set G(Z, X) = [Z, X] for any space Z with cat $Z{\leq}k$. In this paper, we introduce a dual concept of $C_k$-space and obtain a dual result of the above result using the dual Gottlieb set and the dual LS category.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.249-257
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• 2013

In this paper, we introduce and study the concepts of $WC^f_k$-spaces with respect to spaces which are generalized concepts of $C^f_k$-spaces for maps, and introduce the dual concepts of $WC^f_k$-spaces with respect to spaces and obtain some dual results.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.135-140
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• 2012

In this paper, we introduce the concepts of $DC^{p}_{k}$-spaces for maps which are the dual concepts of $C^{f}_{k}$-spaces for maps, and characterize $DC^{p}_{k}$-spaces for maps using the dual Gottlieb sets for maps and the LS cocategories.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.735-743
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• 2014

We obtain a splitting theorem which characterizes when a given space is a catesian product of an $H^f$-space, and also obtain a dual theorem for a co-$H^g$-space. Then we get Dula and Gottlieb's results as corollaries.

• 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.

• 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.