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- 저자 : 윤연수 (검색결과 20 건)
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PRINCIPAL FIBRATIONS AND GENERALIZED H-SPACES
윤연수 충청수학회 2016 충청수학회지 Vol.29 No.1
For a map $f:A\to X$, there are concepts of $H^{f}$-spaces, $T^{f}$-spaces, which are generalized ones of $H$-spaces [17,18]. In general, Any $H$-space is an $H^{f}$-space, any $H^{f}$-space is a $T^{f}$-space. For a principal fibration $E_{k}\to X$ induced by $k:X\to X'$ from $\epsilon :PX'\to X'$, we obtain some sufficient conditions to having liftings $H^{\bar{f}}$-structures and $T^{\bar{f}}$-structures on $E_{k}$ of $H^{f}$-structures and $T^{f}$-structures on $X$ respectively. We can also obtain some results about $H^{f}$-spaces and $T^{f}$-spaces in Postnikov systems for spaces, which are generalizations of Kahn's result about $H$-spaces.
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윤연수 충청수학회 2023 충청수학회지 Vol.36 No.4
'In this paper, we study some properties about Cfk-structures and obtain a sufficient condition to be lifting Cfk -structure, nand using the above result, we can obtain a Stasheff’s result about to be lifting H-structure as a corollary
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Lifting T-structures and their duals
윤연수 충청수학회 2007 충청수학회지 Vol.20 No.3
We define and study a concept of $T^{f}$-space for a map, which is a generalized one of a $T$-space, in terms of the Gottlieb set for a map. We show that $X$ is a $T^{f}$-space if and only if $G(\Sigma B;A,f,X)=[\Sigma B,X]$ for any space $B$. For a principal fibration $E_{k}\to X$ induced by $k:X\to X'$ from $\epsilon :PX'\to X'$, we obtain a sufficient condition to having a lifting $T^{\bar{f}}$-structure on $E_{k}$ of a $T^{f}$-structure on $X$ . Also, we define and study a concept of co-$T^{g}$-space for a map, which is a dual one of $T^{f}$-space for a map. We obtain a dual result for a principal cofibration $i_{r}:X\to C_{r}$ induced by $r:X'\to X$ from $\iota: X'\to cX'$.
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Hf -Spaces for Maps and Their Duals
윤연수 한국수학교육학회 2007 純粹 및 應用數學 Vol.14 No.4
We define and study a concept of Hf -space for a map, which is a gener- alized concept of an H-space, in terms of the Gottlieb set for a map. For a principal fibration Ek ! X induced by k : X ! X′ from ǫ : PX′ ! X′, we can obtain a sufficient condition to having an H ¯ f -structure on Ek, which is a generalization of Stasheff’s result [17]. Also, we define and study a concept of co-Hg-space for a map, which is a dual concept of Hf -space for a map. Also, we get a dual result which is a generalization of Hilton, Mislin and Roitberg’s result [6].
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G0 p-SPACES FOR MAPS AND HOMOLOGY DECOMPOSITIONS
윤연수 충청수학회 2015 충청수학회지 Vol.28 No.4
For a map p : X ! A, we dene and study a concept of G0 p-space for a map, which is a generalized one of a G0-space. Any G0-space is a G0 p-space, but the converse does not hold. In fact, CP2 is a G0 -space, but not a G0-space. It is shown that X is a G0 p-space if and only if Gn(X; p;A) = Hn(X) for all n. We also obtain some results about G0 p-spaces and homology decompositions for spaces. As a corollary, we can obtain a dual result of Haslam's result about G-spaces and Postnikov systems.
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CATEGORY OF MAPS AND GOTTLIEB SETS FOR MAPS, AND THEIR DUALS
윤연수 충청수학회 2013 충청수학회지 Vol.26 No.1
In this paper, we introduce and study the concepts of WCf k -spaces with respect to spaces which are generalized concepts of Cf k -spaces for maps, and introduce the dual concepts of WCf k -spaces with respect to spaces and obtain some dual results.
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Principal cofibrations and generalized co-H-spaces
윤연수 충청수학회 2017 충청수학회지 Vol.30 No.1
For a map p : X → A, there are concepts of co-Hpspaces, co-Tp-spaces, which are generalized ones of co-H-spaces [17,18]. For a principal cofibration ir : X → Cr induced by r : X′ → X from ι : X′ → cX′, we obtain some sufficient conditions to having extensions co-H¯ p-structures and co-T ¯ p-structures on Cr of co-Hp-structures and co-Tp-structures on X respectively. We can also obtain some results about co-Hp-spaces and co-Tp-spaces in homology decompositions for spaces, which are generalizations of Golasinski and Klein’s result about co-H-spaces.
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On cocyclic maps and cocategory
윤연수 충청수학회 2011 충청수학회지 Vol.24 No.1
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 Z ≤ 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.
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GENERALIZED DUAL GOTTLIEB SETS AND COCATEGORIES
윤연수,김학도 충청수학회 2012 충청수학회지 Vol.25 No.1
In this paper, we introduce the concepts of $DC_{k}^{p}$-spaces for maps which are the dual concepts of $C_{k}^{f}$-spaces for maps, and characterize $DC_{k}^{p}$-spaces for maps using the dual Gottlieb sets for maps and the $LS$ cocategories.
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Weak co-$T$-cofibrations and homology decompositions
윤연수 충청수학회 2018 충청수학회지 Vol.31 No.2
In this paper, we define a concept of weak co-$T$-cofibration which is a generalization of weak $H'$-cofibration, and study some properties of weak co-$T$-cofibration and relations between the weak co-$T$-cofibration and the homology decomposition for a cofibration.
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