• Korean Journal of Mathematics
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• v.26 no.4
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• pp.709-727
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• 2018

Here we have studied the ideas of $g^*$-closed sets, $g{\bigwedge}_{{\tau}^-}$ sets and ${\lambda}^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied some separation axioms like $T_{\frac{\omega}{4}}$, $T_{\frac{3\omega}{8}}$, $T_{\omega}$ in Alexandroff spaces and also have introduced a new separation axiom namely $T_{\frac{5\omega}{8}}$ axiom in this space.

• 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.

• 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].

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.13-19
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• 2005

In this paper we introduce the notions of g-regularity and g-normality in fuzzy topological spaces. We obtain some characterizations and several preservation theorems of such spaces.

• East Asian mathematical journal
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• v.24 no.4
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• pp.317-328
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• 2008

In this paper we introduce ${\pi}G{\alpha}$-LC sets, ${\pi}G{\alpha}-LC^*$ sets and ${\pi}G{\alpha}-LC^{**}$ sets and different notions of generalizations of continuous functions in topological space and discuss some of their properties. Further we prove pasting lemma for ${\pi}G{\alpha}-LC^{**}$ continuous functions and ${\pi}G{\alpha}-LC^{**}$ irresolute functions.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.1-9
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• 2011

The notion of ${\tilde{g}}{\alpha}$-closed sets in a topological space introduced by R. Devi and A. selvakumar [2]. In this paper, we introduce the concept of ${\tilde{g}}{\alpha}$-US spaces by utilizing ${\tilde{g}}{\alpha}$-open sets and study the basic properties of this space.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.3
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• pp.255-263
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• 2006

In this paper, we introduce the concepts of ${\gamma}$-fuzzy feebly open and ${\gamma}$-fuzzy feebly closed sets in Sostak's fuzzy topological spaces and by using them, we explain the notions of ${\gamma}$-fuzzy F-closed spaces. Also, we give some characterization of ${\gamma}$-fuzzy F-closedness in terms of fuzzy filterbasis and ${\gamma}$-fuzzy feebly-${\theta}$-cluster points.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.173-188
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• 2014

In this paper, a new class of open sets, namely ${\gamma}^*$-pre-open sets was introduced and its basic properties were studied. Moreover a new type of topology ${\tau}_{{\gamma}p^*}$ was generated using ${\gamma}^*$-pre-open sets and characterized the resultant topological space (X, ${\tau}_{{\gamma}p^*}$) as ${\gamma}^*$-pre-$T_{\frac{1}{2}}$ space.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.369-373
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• 1995

We introduce the concepts of generalized closed fuzzy set(breifly g-closed fuzzy set) and generalized fuzzy continuity (briefly g-fuzzy continuity), and investigate their some properties. When A is a fuzzy set in a fuzzy topological space, we denote the closure of A, the interior of A and the complement of A as CA(a) and CA, respectively

• Kyungpook Mathematical Journal
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• v.33 no.2
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• pp.205-209
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• 1993