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우무하,이기영 대한수학회 2000 대한수학회논문집 Vol.15 No.2
이 논문에서 계치부분군의 일반화와 이들을 이용한 G-열의 도입과정을 다룬다. 계치부분군과 일반화된 계치부분군 그리고 호모토피군의 차이를 설명하여 몇가지 공간의 계치부분군을 계산한다. 그리고 G-열이 완전열이 되기 위한 조건들을 조사하고 이 완전성을 이용하여 계치부분군의 계산과 함수의 단사성과 그 함수의 G-열의 완전성과의 상호 관련성을 보인다. 마지막으로 G-열의 일반화와 쌍대 G-열의 다룬다.
Mappings From Metacompact Spaces
禹茂夏 계명대출판부 1979 童山申泰植博士古稀紀念論叢 Vol.S No.-
It is shown that the image of a paracompact space under an almost-open compact mapping is metacompact. By strengthening the mapping from compact to finite-to-one the following results are also obtained. The image of a (countably) metacompact space under an almost (pseudo)-open finite-to-one mapping is (countably) metacompact. Notation and terminology will follow that of J. 1. Kelley (7) and all mappings will be continuous and surjective. We denote the interior of a subset A of a topological space by Int A.
CERTAIN GENERALIZATIONS OF G-SEQUENCES AND THEIR EXACTNESS
이기영,우무하,Xuezhi Zhao 대한수학회 2008 대한수학회보 Vol.45 No.1
In this paper, we generalize the Gottlieb groups and the re-lated G-sequence of those groups, and present some sucient conditionsto ensure the exactness or non-exactness of G-sequences at some terms.We also give some applications of the exactness or non-exactness of G-sequences. Especially, we show that the non-exactness of G-sequencesimplies the non-triviality of homotopy groups of some function spaces.
Gottlieb Groups and Subgroups of the Group of Self-Homotopy Equivalences
김재룡,Nobuyuki Oda,Jianzhong Pan,우무하 대한수학회 2006 대한수학회지 Vol.43 No.5
mathcal{E}(X) consisting of homotopy classes of self-homotopyequivalences that fix homotopy groups through the dimension of X andmathcal{E}_*(X) be the subgroup of mathcal{E} (X) that fix homologygroups for all dimension.In this paper, we establish some connections between the homotopy group of Xand the subgroup mathcal{E}_#(X)cap mathcal{E}_*(X) ofmathcal{E}(X).We also give some relations between pi_n (W),as well as a generalized Gottlieb group G_n^f(W,X),and a subset mathcal{M}{_{#}^f}_N (X, W) of [X, W]. Finally weestablish a connection between the coGottlieb group of X andthe subgroup of mathcal{E}(X) consisting of homotopy classes of self-homotopyequivalences that fix cohomology groups.