• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.3
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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.

• East Asian mathematical journal
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• v.29 no.1
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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 ${\beta}{\Lambda}X={\Lambda}{\beta}X$.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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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.

• 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.

• 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.

• 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.

• The Mathematical Education
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• v.21 no.1
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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.

• 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 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.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.17-29
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• 2022

A commutative ring with unity R is called an EM-ring if for any finitely generated ideal I there exist a in R and a finitely generated ideal J with Ann(J) = 0 and I = aJ. In this article it is proved that C(X) is an EM-ring if and only if for each U ∈ Coz (X), and each g ∈ C^* (U) there is V ∈ Coz (X) such that U ⊆ V, ${\bar{V}}=X$, and g is continuously extendable on V. Such a space is called an EM-space. It is shown that EM-spaces include a large class of spaces as F-spaces and cozero complemented spaces. It is proved among other results that X is an EM-space if and only if the Stone-Čech compactification of X is.