• 호남수학학술지
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• 제39권4호
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• pp.655-663
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• 2017

In this paper we define $AP_c$ and $AP_{cc}$ spaces which are stronger than the property of approximation by points(AP). We investigate operations on their subspaces and study function theorems on $AP_c$ and $AP_{cc}$ spaces. Using those results, we prove that every continuous image of a countably compact Hausdorff space with AP is AP. Finally, we prove a theorem that every compact ${\kappa}$-WAP space is ${\kappa}$-pseudoradial, and prove a theorem that the product of a compact ${\kappa}$-radial space and a compact ${\kappa}$-WAP space is a ${\kappa}$-WAP space.

• 대한수학회보
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• 제48권5호
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• pp.1105-1109
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• 2011

We establish a result concerning simultaneous approximation and interpolation from certain uniformly dense subsets of the space of vector-valued continuous functions vanishing at infinity on locally compact Hausdorff spaces.

• 대한수학회지
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• 제33권1호
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• pp.155-167
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• 1996

Let X be a compact Hausdorff space, C(X) denote the set of all continuous real valued functions on X and $\ell \in N$ be any natural number.

• 대한수학회지
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• 제45권1호
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• pp.197-204
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• 2008

We study diameter preserving linear maps from C(X) into C(Y) where X and Y are compact Hausdorff spaces. By using the extreme points of $C(X)^*\;and\;C(Y)^*$ and a linear condition on them, we obtain that there exists a diameter preserving linear map from C(X) into C(Y) if and only if X is homeomorphic to a subspace of Y. We also consider the case when X and Y are noncompact but locally compact spaces.

• 충청수학회지
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• 제24권3호
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• pp.457-467
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• 2011

In this paper, we establish some comparison theorems about volumes of tubes in metric spaces with nonpositive curvature. First we compare the Hausdorff measure of tube about a metric ball contained in an (n-1)-dimensional totally geodesic subspace of an n-dimensional locally compact, geodesically complete Hadamard space with Lebesgue measure of its corresponding tube in Euclidean space ${\mathbb{R}}^n$, and then develop the result to the case of an m-dimensional totally geodesic subspace for 1 < m < n with an additional condition. Also, we estimate the Hausdorff measure of the tube about a shortest curve in a metric space of curvature bounded above and below.

• 한국수학교육학회지시리즈A:수학교육
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• 제16권2호
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• pp.22-26
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• 1978

($\alpha$$_{x}$, $\alpha$X)와 ($\alpha$$_{Y}$ , $\alpha$Y)를 T$_2$ 공간 X와 Y의 Alexandroff base Compactification이라 할 때 $\alpha$fㆍ$\alpha$$_{x}$=$\alpha$$_{Y}$ f를 만족하는 open이고 연속인 함수 $\alpha$f:$\alpha$X$\longrightarrow$$\alpha$Y가 존재하는 연속함수 f:X$\longrightarrow$Y는 유일한 $\alpha$-extension $\alpha$f를 가지며 Category ABC를 T$_2$ 공간과 위와 같은 연속함수 f들의 Category라고 할 때 open이고 연속인 함수와 Compact space들의 Category는 Category ABC의 epireflective subcategory임을 밝혔다.

• 호남수학학술지
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• 제27권4호
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• pp.631-639
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• 2005

For compact Hausdorff spaces X and Y let C(X) and C(Y) denote the complex Banach spaces of complex valued continuous functions on X and Y, respectively. Also let $T:C(X){\rightarrow}C(Y)$ be a linear isomerty. Necessary and sufficient conditions are given such that range of T has finite codimension.

• 대한수학회논문집
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• 제22권4호
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• pp.569-573
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• 2007

In this note, we construct an example of a Hausdorff K-starcompact (hence, $1\frac{1}{2}$-star-compact) space X having a regular closed $G_{\delta}-subset$ which is not $1\frac{1}{2}$-starcompact (hence, not K-starcompact).

• 충청수학회지
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• 제36권4호
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• pp.279-288
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• 2023

We obtain a Chandrabhan type fixed point theorem for a multimap having a non-compact domain and a weakly closed graph, and taking convex values only on a quasi-convex subset of Hausdorff locally convex topological vector space. We introduce the definition of Chandrabhan-set and find a sufficient condition for every countably condensing multimap to have a relatively compact Chandrabhan-set. Finally, we establish a new version of Sadovskii fixed point theorem for multimaps.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.25-40
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• 2021

In this article we introduce tribonacci sequence spaces c0(T) and c(T) derived by the domain of a newly defined regular tribonacci matrix T. We give some topological properties, inclusion relations, obtain the Schauder basis and determine ��-, ��- and ��- duals of the spaces c0(T) and c(T). We characterize certain matrix classes (c0(T), Y) and (c(T), Y), where Y is any of the spaces c0, c or ℓ∞. Finally, using Hausdorff measure of non-compactness we characterize certain class of compact operators on the space c0(T).