• 충청수학회지
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• 제22권4호
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• pp.831-841
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• 2009

For a map f : A $\rightarrow$ X, we define and study a concept of $G^f$-space for a map, which is a generalized one of a G-space. Any G-space is a $G^f$-space, but the converse does not hold. In fact, $S^2$ is a $G^{\eta}$-space, but not G-space. We show that X is a $G^f$-space if and only if $G_n$(A, f,X) = $\pi_n(X)$ for all n. It is clear that any $H^f$-space is a $G^f$-space and any $G^f$-space is a $W^f$-space. We can also obtain some results about $G^f$-spaces in Postnikov systems for spaces, which are generalization of Haslam's results about G-spaces.

• 충청수학회지
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• 제28권4호
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• pp.603-614
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• 2015

For a map $p:X{\rightarrow}A$, we define and study a concept of $G^{\prime}_p$-space for a map, which is a generalized one of a G'-space. Any G'-space is a $G^{\prime}_p$-space, but the converse does not hold. In fact, $CP^2$ is a $G^{\prime}_{\delta}$-space, but not a G'-space. It is shown that X is a $G^{\prime}_p$-space if and only if $G^n(X,p,A)=H^n(X)$ for all n. We also obtain some results about $G^{\prime}_p$-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.

• 대한수학회지
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• 제37권6호
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• pp.885-899
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• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.793-806
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• 2016

G-vector-valued sequence space frames and g-Banach frames for Banach spaces are introduced and studied in this paper. Also, the concepts of duality mapping and ${\beta}$-dual of a BK-space are used to define frame mapping and synthesis operator of these frames, respectively. Finally, some results regarding the existence of g-vector-valued sequence space frames and g-Banach frames are obtained. In particular, it is proved that if X is a separable Banach space and Y is a Banach space with a Schauder basis, then there exist a Y-valued sequence space $Y_v$ and a g-Banach frame for X with respect to Y and $Y_v$.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.517-524
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• 2012

In this paper, we first show that for any space X, there is a Boolean subalgebra $\mathcal{G}(z_X)$ of R(X) containg $\mathcal{G}(X)$. Let X be a strongly zero-dimensional space such that $z_{\beta}^{-1}(X)$ is the minimal cloz-coevr of X, where ($E_{cc}({\beta}X)$, $z_{\beta}$) is the minimal cloz-cover of ${\beta}X$. We show that the minimal cloz-cover $E_{cc}(X)$ of X is a subspace of the Stone space $S(\mathcal{G}(z_X))$ of $\mathcal{G}(z_X)$ and that $E_{cc}(X)$ is a strongly zero-dimensional space if and only if ${\beta}E_{cc}(X)$ and $S(\mathcal{G}(z_X))$ are homeomorphic. Using these, we show that $E_{cc}(X)$ is a strongly zero-dimensional space and $\mathcal{G}(z_X)=\mathcal{G}(X)$ if and only if ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• 대한수학회보
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• 제21권2호
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• pp.67-75
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• 1984

Let X be a topological space. We consider a groupoid G over X and the quotient groupoid G/N for any normal subgroupoid N of G. The concept of groupoid (topological groupoid) is a natural generalization of the group(topological group). An useful example of a groupoid over X is the foundamental groupoid .pi.X whose object group at x.mem.X is the fundamental group .pi.(X, x). It is known [5] that if X is locally simply connected, then the topology of X determines a topology on .pi.X so that is becomes a topological groupoid over X, and a covering space of the product space X*X. In this paper the concept of the locally simple connectivity of a topological space X is applied to the groupoid G over X. That concept is defined as a term '1-connected local subgroupoid' of G. Using this concept we topologize the groupoid G so that it becomes a topological groupoid over X. With this topology the connected groupoid G is a covering space of the product space X*X. Further-more, if ob(.overbar.G)=.overbar.X is a covering space of X, then the groupoid .overbar.G is also a covering space of the groupoid G. Since the fundamental groupoid .pi.X of X satisfying a certain condition has an 1-connected local subgroupoid, .pi.X can always be topologized. In this case the topology on .pi.X is the same as that of [5]. In section 4 the results on the groupoid G are generalized to the quotient groupoid G/N. For any topological groupoid G over X and normal subgroupoid N of G, the abstract quotient groupoid G/N can be given the identification topology, but with this topology G/N need not be a topological groupoid over X [4]. However the induced topology (H) on G makes G/N (with the identification topology) a topological groupoid over X. A final section is related to the covering morphism. Let G$_{1}$ and G$_{2}$ be groupoids over the sets X$_{1}$ and X$_{2}$, respectively, and .phi.:G$_{1}$.rarw.G$_{2}$ be a covering spimorphism. If X$_{2}$ is a topological space and G$_{2}$ has an 1-connected local subgroupoid, then we can topologize X$_{1}$ so that ob(.phi.):X$_{1}$.rarw.X$_{2}$ is a covering map and .phi.: G$_{1}$.rarw.G$_{2}$ is a topological covering morphism.

• 대한수학회지
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• 제47권1호
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• pp.215-222
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• 2010

A T$_1$ topological space X is called an almost GP-space if every dense G$_{\delta}$-set of X has nonempty interior. The behaviour of almost GP-spaces under taking subspaces and superspaces, images and preimages and products is studied. If each dense G$_{\delta}$-set of an almost GP-space X has dense interior in X, then X is called a GID-space. In this paper, some interesting properties of GID-spaces are investigated. We will generalize some theorems that hold in almost P-spaces.

• 융합신호처리학회논문지
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• 제11권3호
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• pp.183-188
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• 2010

본 논문에서는 LoG scale-space를 이용한 그레이스케일 영상에서 연속패턴 라인 중심축 검출 기법을 제안한다. 제안된 기법은 LoG의 스케일 크기를 적응적으로 가변하여 라인 중심축을 검출하는 방법이다. 작은 스케일의 LoG 연산자는 라인의 에지점에서 영교차 특성이 나타나며, 영교차점을 중심으로 좌우에 +/- 극성을 가진 극점이 존재하게 된다. 즉 일정한 폭을 가지는 라인은 양쪽 가장자리에서 2개의 +극점을 가지게 된다. LoG의 확산동작을 반복함에 따라 스케일을 증가시키면 +극점은 라인 양쪽 에지영역에서 중심영역으로 이동하여 점진적으로 가까워져서 최종적으로 하나의 극점으로 중첩되어진다. 연속패턴 라인 중심축은 2개의 +극점이 중심영역에서 중첩되는 점이다. 제안하는 방법은 기존의 이진영상에서 적용되는 세선화 방법보다 강인하게 연속패턴 라인 중심축을 검출함을 확인하였다.

• 대한수학회지
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• 제35권2호
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

• 대한수학회논문집
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• 제9권4호
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• pp.933-944
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• 1994

Let $\pi : P \to S^4$ be a principal G-bundle over $S^4$ whose the structure group G is a compact, connected, simple Lie group. Since $\pi_3(G) = \pi_4 (BG) = Z$, we can classify the principal bundle $P_k$ over $S^4$ by the map $S^4 \to BG$ of degree k. Atiyah and Jones [2] showed that $C_k = A_k/g^b_k$ is homotopy equivalent to $\Omega^3_k G \simeq \Omega^4_k BG$ where $A_k$ is the space of the all connections in $P_k$ and $g^b_k$ is the based gauge group which consists of all base point preserving automorphisms on $P_k$. Here $\Omega^nX$ is the space of all base-point preserving continuous map from $S^n$ to X. Let $M_k$ be the space of based gauge equivalence classes of all connections in $P_k$ satisfying the Yang-Mills self-duality equations, which we call the moduli space of G instantons.