• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.351-359
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• 2019

In this paper, we introduce a modification of extremally disconnected spaces which is said to be m-extremally disconnected. And we obtain many characterizations of m-extremally disconnected spaces. The concepts of ${\ast}$-extremally disconnected spaces, ${\ast}$-hyperconnected spaces, and generalized hyperconnectedness are as examples for this paper.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.175-182
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• 2008

This paper is a revised version of [5]. In [5], we define' nearness between two points' in a topological space in many ways and show that a continuous function preserves one-sided nearness. We also show that a $T_1$-space is characterized by one-sided nearness exactly. In this paper, we introduce extremally disconnected spaces and show that the new topology generated by the set of equivalence classes as a base is extremally disconnected.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.209-212
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• 2005

In this paper, we introduce the concept of fuzzy quasi extremally disconnectedness in fuzzy bitopological space, which is a generalization of fuzzy extremally disconnectedness due to Ghosh [5] in fuzzy topological space and investigate some of its properties using the concepts of quasi-semi-closure, quasi-$\Theta$_closure and related notions in a fuzzy bitopological setting.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.117-124
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• 1993

In this paper, we introduce a concept of quasi $O_{z}$ -spaces which generalizes that of $O_{z}$ -spaces. Indeed, a completely regular space X is a quasi $O_{z}$ -space if for any regular closed set A in X, there is a zero-set Z in X with A = c $l_{x}$ (in $t_{x}$ (Z)). We then show that X is a quasi $O_{z}$ -space iff every open subset of X is $Z^{#}$-embedded and that X is a quasi $O_{z}$ -spaces are left fitting with respect to covering maps. Observing that a quasi $O_{z}$ -space is an extremally disconnected iff it is a cloz-space, the minimal extremally disconnected cover, basically disconnected cover, quasi F-cover, and cloz-cover of a quasi $O_{z}$ -space X are all equivalent. Finally it is shown that a compactification Y of a quasi $O_{z}$ -space X is again a quasi $O_{z}$ -space iff X is $Z^{#}$-embedded in Y. For the terminology, we refer to [6].[6].

• Journal for History of Mathematics
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• v.17 no.2
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• pp.73-84
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• 2004

Stone introduced extremally disconnected spaces as the image of complete Boolean algebras under his famous duality between Bool and ZComp and they turn out to be projective objects in various categories of Hausdorff spaces and completely regular ones are exactly those X with Dedekind complete C(X, ). In the pointfree setting, extremally disconnected frame (= De Morgan frame) are those with De Morgan condition. In this paper, we investigate a historical aspect of De Morgan frame together with that of De Morgan.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.77-82
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• 1998

In this paper, we introduce the concept of quasi-fuzzy extremally disconnectedness in fuzzy bitopological space, which is a generalization of fuzzy extremally disconnectedness due to Ghosh [5] in fuzzy topological space and invetstigate some of its properties using the concepts of quasi-semi-closure, quasi-$\theta$-closure and related notions in a fuzzy bitopological settings.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.59-68
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• 2018

In this paper, We define and explore the characterizations and properties of soft regular open(closed) and soft semi-regular sets in soft topological spaces. The properties of soft extremally disconnected spaces are also introduced and discussed. The findings in this paper will help researcher to enhance and promote further study on soft topology to carry out a general framework for their applications in practical life.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.95-97
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• 1983

In this paper, we show a necessary and sufficient condition for QHC spaces to be S-closed. T. Thomson introduced S-closed spaces in [2]. A topological space X is said to be S-closed if every semi-open cover of X admits a finite subfamily such that the closures of whose members cover the space, where a set A is semi-open if and only if there exists an open set U such that U.contnd.A.contnd.Cl U. A topological space X is quasi-H-closed (denote QHC) if every open cover has a finite subfamily whose closures cover the space. If a topological space X is Hausdorff and QHC, then X is H-closed. It is obvious that every S-closed space is QHC but the converse is not true [2]. In [1], Cameron proved that an extremally disconnected QHC space is S-closed. But S-closed spaces are not necessarily extremally disconnected. Therefore we want to find a necessary and sufficient condition for QHC spaces to be S-closed. A topological space X is said to be semi-locally S-closed if each point of X has a S-closed open neighborhood. Of course, a locally S-closed space is semi-locally S-closed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.1-6
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• 2010

The notion of $\star$-Externally disconnected fuzzy ideal topological spaces is introduced and studied. Many characterizations of the space are obtained.

• Journal of Industrial Technology
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• v.4
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• pp.25-27
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• 1984

위상 공간 X의 모든 Semi-open cover에 대하여 그들의 closure의 합이 X를 cover한 유한 부분 속이 존재할 때 위상 공간X를 S-closed라고 한다. 이 논문에서는 S-closed와 semi-closed set 사이의 관계를 조사하였고 Haussdorff 공간과 S-closed 공간에서 extremally disconnected와 semi-continuous의 성질을 조사하였다.