• 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.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 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.