• 충청수학회지
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• 제27권3호
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• pp.363-379
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• 2014

In this paper, introducing various separation axioms on a bi-GTS, it has been observed that such separation axioms actually unify the well-known separation axioms on topological spaces. Several characterizations of such separation properties of a bi-GTS are established in terms of ${\gamma}_{{\mu}_i,{\mu}_j}$-closure operator, generalized cluster sets of functions and graph of functions.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2002년도 추계학술대회 및 정기총회
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• pp.51-54
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• 2002

We investigate some properties of the separation axioms in fuzzy topological spaces.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2002년도 추계학술대회 및 정기총회
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• pp.59-62
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• 2002

We investigate some relations between the separation axioms in fuzzy topological spaces and one in fuzzy hyperspaces.

• East Asian mathematical journal
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• 제27권5호
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• pp.507-512
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• 2011

In this paper gpr-open sets are used to define some weak separation axioms and we study some of their basic properties. The implications of these axioms among themselves are also verified.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 춘계학술대회 학술발표 논문집
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• pp.47-51
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• 1997

In this paper, certain fuzzy semi-separation axioms are studied in terms of the notions of quasi-coincidence, fuzzy semi-q-neigborhoods and fuzzy semi-$\theta$-closure operators. Fuzzy semi-T2, fuzzy semi-Urysohn and fuzzy s-regular spaces are defined, and fuzzy spaces satisfying these axioms are characterized.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권2호
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• pp.115-127
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• 2009

In the present paper we introduce and study L-pre-$T_0$-, L-pre-$T_1$-, L-pre-$T_2$ (L-pre-Hausdorff)-, L-pre-$T_3$ (L-pre-regularity)-, L-pre-$T_4$ (L-pre-normality)-, L-pre-strong-$T_3$-, L-pre-strong-$T_4$-, L-pre-$R_0$-, L-pre-$R_1$-separation axioms in (2, L)-topologies where L is a complete residuated lattice.Sometimes we need more conditions on L such as the completely distributive law or that the "$\bigwedge$" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results(see[1,2]) are generalized and new consequences are obtained.

• 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.

• 대한수학회논문집
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• 제24권3호
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• pp.433-450
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• 2009

We introduce a new concept of intuitionistic fuzzy topological subspace, which coincides with the usual concept of intuitionistic fuzzy topological subspace due to Samanta and Mondal [18] in the case that $\mu=X_A$ for A $\subseteq$ X. Also, we introduce and study some concepts such as continuity, separation axioms, compactness and connectedness in this sense.

• 대한수학회보
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• 제36권4호
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• pp.723-736
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• 1999

The paper is devoted to generalizations of continuity of set-valued mappings and some properties of hypertopologies on the collection of some subsets of a topological space. It is also dedicated to continuous selection theorems without relatively higher separation axioms. More precisely, we give characterizations of $\lambda$-collectionwise normality using continuous functions as in Michael's papers.

• 대한수학회논문집
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• 제32권1호
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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.