• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.623-628
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• 2010

Nakaoka and Oda ([1] and [2]) introduced the notion of maximal open sets and minimal closed sets in topological spaces. In this paper, we introduce new classes of sets called maximal $\theta$-open sets, minimal $\theta$-closed sets, $\theta$-semi maximal open and $\theta$-semi minimal closed and investigate some of their fundamental properties.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.377-384
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• 2012

In this paper some properties of sequentially closed sets and $k$-closed sets in a topological space are discussed, it is shown that a space is a $k$-quotient image of a metric space if and only if its each sequentially closed set is $k$-closed, and some related examples about connectedness are obtained.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.34-37
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• 2001

Park et al. [Proc. KFIS Fall Conf. 10(2) (2000), 59-62] defined fuzzy ${\gamma}$-open sets by using an operation ${\gamma}$ on a fts (X, $\tau$) and investigated the related fuzzy topological properties of the associated fuzzy topology $\tau$/seb ${\gamma}$/ and $\tau$. As generalizations of the notion of fuzzy ${\gamma}$-closed sets, we define gf. ${\gamma}$-closed sets and g*f. ${\gamma}$-closed sets and study basic properties of these sets relative to union and intersection. Also, we introduce and study two classes of ftss called fuzzy ${\gamma}$-T* and fuzzy ${\gamma}$-T$_{1}$2/ spaces by using the notions of gf. ${\gamma}$-closed and g*f. ${\gamma}$-closed sets.

• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.187-192
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• 2009

In this paper, we introduce the notions of $s{\gamma}$-generalized closed sets and $s{\gamma}$-generalized sets, and investigate some properties for such notions.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1259-1265
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• 2016

In this paper, we introduce the notions of mean open and closed sets in topological spaces, and obtain some properties of such sets. We observe that proper paraopen and paraclosed sets are identical to mean open and closed sets respectively.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.41-54
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• 2007

In this paper, we introduce the notion of $g{\cdot}{\gamma}$-closed sets and study its basic properties. Also we introduce the notion of ${\gamma}-T_*$ spaces and investigate relationships among these spaces and ${\gamma}-T_i$ spaces (i = 0,1/2,1) due to Ogata [5].

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.175-181
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• 2017

In this paper, we introduce a notion of cleanly covered topological spaces along with two strong separation axioms. Some properties of cleanly covered topological spaces are obtained in term of maximal open sets including some similar properties of a topological space in term of maximal closed sets. Two strong separation axioms are also investigated in terms of minimal open and maximal closed sets.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.183-191
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• 2018

This paper deals with binary ideal topological space and discuss about generalized binary closed sets and generalized kernel in the same topological space. Further it will discuss various types of characterizations of generalized binary closed sets and generalized kernel.

• 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.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.437-453
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• 2017

A new class of sets, called generalized (${\Lambda}$, b)-closed sets, has been introduced and studied. Also, several properties of generalized (${\Lambda}$, b)-closed sets are investigated. Some characterizations of ${\Lambda}_b$-regular spaces and ${\Lambda}_b$-normal spaces are discussed.