• Korean Journal of Mathematics
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• 제26권4호
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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.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.405-412
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• 2012

The purpose of the present paper is towards working out a unified version of the study of certain weak forms of generalized open sets and their neighbouring forms, as are already available in the literature. In terms of an operation, as initiated by $\acute{A}$. Cs$\acute{a}$sz$\acute{a}$r, we introduce unified definitions of ${\wedge}_{\psi}$-sets, ${\vee}_{\psi}$-sets, $g{\cdot}{\wedge}_{\psi}$-sets and $g{\cdot}{\vee}_{\psi}$-sets and derive results concerning them.

• 충청수학회지
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• 제24권1호
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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.

• Kyungpook Mathematical Journal
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• 제54권2호
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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.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 춘계학술대회 학술발표 논문집
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권1호
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• pp.35-47
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• 2019

The purpose of this paper is to introduce and study new notions of continuity, compactness and stability in ditopological texture spaces based on the notions of ${\beta}$-g-open and ${\beta}$-g-closed sets and some of their characterizations are obtained. Finally, the relationships between these concepts and the other related concepts are investigated.

• Korean Journal of Mathematics
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• 제29권2호
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• pp.355-360
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• 2021

In this paper, we introduce the definition of sequentially g-connected components and sequentially locally g-connected by using sequentially g-closed sets. Moreover, we investigate some characterization of sequentially g-connected components and sequentially locally g-connected.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권3호
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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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• 제61권2호
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• pp.371-381
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• 2021

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L²(G) and, using the scaling function, we construct an orthonormal wavelet basis for L²(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.

• 호남수학학술지
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• 제39권1호
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• pp.101-113
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• 2017

Let G be a semialgebraic group which is not necessarily compact. Let X be a proper semialgebraic G-set whose orbit space has a semialgebraic structure. In this paper we prove that X has a finite open straight G-CW complex structure.