• Honam Mathematical Journal
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• v.32 no.2
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• pp.307-331
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• 2010

The notion of intuitionistic fuzzy semi-pre interior (semi-pre closure) is introduced, and several related properties are investigated. Characterizations of an intuitionistic fuzzy regular open set, an intuitionistic fuzzy semi-open set and an intuitionistic fuzzy ${\gamma}$-open set are provided. A method to make an intuitionistic fuzzy regular open set (resp. intuitionistic fuzzy regular closed set) is established. A relation between an intuitionistic fuzzy ${\gamma}$-open set and an intuitionistic fuzzy semi-preopen set is considered. A condition for an intuitionistic fuzzy set to be an intuitionistic fuzzy ${\gamma}$-open set is discussed.

• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.21-30
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• 1992

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.71-78
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• 2000

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.2
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• pp.257-261
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• 2010

In this paper, we introduce the concept of fuzzy r-generalized almost continuous mapping and obtain some characterizations of such a mapping. In particular, we investigate characterizations for the fuzzy r-generalized almost continuity by using the concept of fuzzy r-generalized regular open sets.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.401-413
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• 2012

In the present paper we construct and introduce a new topology from an old one which are independent each of the other. The members of this topology are called ${\omega}_{\delta}$-open sets. We investigate some basic properties and their relationships with some other types of sets. Furthermore, a new characterization of regular and semi-regular spaces are obtained. Also, we introduce and study some new types of continuity, and we obtain decompositions of some types of continuity.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.103-113
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• 2022

The notions of soft rough pre open set, soft rough pre closed set, soft rough dense set, soft rough sub maximal, soft rough pre interior and soft rough pre closure are introduced and studied. We also investigate some related properties of these concepts.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.205-210
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• 2001

We give a characterization of regular operators that allows us to prove that a bounded operator acting between Banach spaces is almost regular if and only if it is regular, solving an open problem in [5]. As an application, we show that some operators in the closure of the set of all regular operators are regular.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.199-203
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• 2010

We introduce the notions of sg-semiopen set and other kinds of generalized sg-open sets and we investigate some properties for such generalized sg-open sets.

• Journal of Industrial Technology
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• v.5
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• pp.47-49
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• 1985

Semi-open을 기초로 하여 만들어진 S-closed 공간의 일반적인 성질을 살펴보고 S-closed 공간과 (maximum) filterbase와의 관계를 조사하였다. 이를 바탕으로 regular closed된 cover C, regular open set인 족(族) C, rc-accumulation, (maximum) filterbase에서의 관계(關係)를 살펴 보았다. Mapping theory에서 almost-open almost-continuous map f가 almost continuous되는 것을 보였다.

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.27-33
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• 1987

Minimal s-Urysohn and minimal s-regular spaces are studied. An s-Urysohn (respectively, s-regular) space (X, $\mathfrak{T}$) is said to be minimal s-Urysohn (respectively, minimal s-regular) if for no topology $\mathfrak{T}^{\prime}$ on X which is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) is s-Urysohn (respectively s-regular). Several characterizations and other related properties of these classes of spaces have been obtained. The present paper is a study of minimal P-spaces where P refers to the property of being an s-Urysohn space or an s-regular space. A P-space (X, $\mathfrak{T}$) is said to be minimal P if for no topology $\mathfrak{T}^{\prime}$ on X such that $\mathfrak{T}^{\prime}$ is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) has the property P. A space X is said to be s-Urysohn [2] if for any two distinct points x and y of X there exist semi-open set U and V containing x and y respectively such that $clU{\bigcap}clV={\phi}$, where clU denotes the closure of U. A space X is said to be s-regular [6] if for any point x and a closed set F not containing x there exist disjoint semi-open sets U and V such that $x{\in}U$ and $F{\subseteq}V$. Throughout the paper the spaces are assumed to be Hausdorff.