• 대한수학회보
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• 제20권2호
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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.

• East Asian mathematical journal
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• 제29권1호
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• pp.83-89
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• 2013

Observing that every Tychonoff space X has a weakly Lindel$\ddot{o}$f extension ${\kappa}X$ and the minimal basically diconneted cover ${\Lambda}{\kappa}X$ of ${\kappa}X$ is weakly Lindel$\ddot{o}$f, we first show that ${\Lambda}_{{\kappa}X}:{\Lambda}{\kappa}X{\rightarrow}{\kappa}X$ is a $z^{\sharp}$-irreducible map and that ${\Lambda}{\beta}X={\beta}{\Lambda}{\kappa}X$. And we show that ${\kappa}{\Lambda}X={\Lambda}{\kappa}X$ if and only if ${\Lambda}^{\kappa}_X:{\kappa}{\Lambda}X{\rightarrow}{\kappa}X$ is an onto map and ${\beta}{\Lambda}X={\Lambda}{\beta}X$.

• 한국지능시스템학회논문지
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• 제8권3호
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• pp.67-70
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• 1998

If there exists a fuzzy continuous function from a fuzzy topological space (X, T) onto the discrete fuzzy toplogical space with two elements, then the space (X, T) is fuzzy disconnected. However, the converse is not true at all. We introduce an example for this and suggest a sufficient condition for which the converse holds.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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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.

• 대한수학회지
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• 제52권2호
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• pp.403-416
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• 2015

An operator T on a complex Hilbert space $\mathcal{H}$ is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for $\mathcal{H}$. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권1호
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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.

• 한국수학사학회지
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• 제17권2호
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• pp.73-84
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• 2004

스톤은 스톤 쌍대성에 의하여 완비 불 대수는 극단적으로 비연결인 콤팩트 하우스도르프 공간에 대응되어 불 대수의 범주 Bool에서 단사 대상은 완비 불 대수인 사실에 의하여 0차원 콤팩트 공간의 범주 ZComp의 사영 대상은 극단적으로 비연결인 콤팩트 공간임을 증명하였고, 완전 정규 공간 X가 극단적인 비연결 공간이기 위한 필요충분조건은 X에서 실직선로의 연속함수의 순서집합 C(X, )이 데데킨트 완비인 사실[6]이 드모르간 틀에서도 성립함을 증명하였다[2]. 이 논문에서는 드 모르간의 역사를 조사하고, 드모르간 틀을 도입하여 극단적인 비연결 공간과의 관계와 드 모르간 틀과 불 대수 사이의 관계를 연구한다.

• 산업기술연구
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• 제4권
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제21권1호
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• pp.19-21
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• 1982

In this paper, we define the z-S-closed spaces using the notions of zero-sets and S-closed spaces introduced by T. Thompson, and investigate some properties of these spaces. We also obtain the following results. If a space X is z-S-closed, then every cover of z-regular semiopen sets has a finite proximate subcover. A z-extremally disconnected z-QHC space is z-S-closed, z-S-closed is contagious.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 추계학술대회 학술발표 논문집
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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.