• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.1-6
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• 2010

The notion of $\star$-Externally disconnected fuzzy ideal topological spaces is introduced and studied. Many characterizations of the space are obtained.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.91-102
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• 1986

A topological space (X,.tau.) is called invertible [7] if for each proper open set U in (X,.tau.) there exists a homoemorphsim h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. Doyle and Hocking [7] and Levine [13], as well as others have investigated properties of invertible spaces. Recently, Crosseley and Hildebrand [5] have introduced the concept of semi-invertibility, which is weaker than that of invertibility, by replacing "homemorphism" in the definition of invertibility with "semihomemorphism", A space (X,.tau.) is said to be semi-invertible if for each proper semi-open set U in (X,.tau.) there exists a semihomemorphism h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. The purpose of the present article is to introduce the class of almost-invertible spaces containing the class of semi-invertible spaces and to investigate its properties. One of the primary concerns will be to determine when a given local property in an almost-invertible space is also a global property. We point out that many of the results obtained can be applied in the cases of semi-invertible spaces and invertible spaces. For example, it is shown that if an invertible space (X,.tau.) has a nonempty open subset U which is, as a subspace, H-closed (resp. lightly compact, pseudocompact, S-closed, Urysohn, Urysohn-closed, extremally disconnected), then so is (X,.tau.).hen so is (X,.tau.).

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.279-292
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• 2022

In this paper we adhere to the definition of infra-topological space as it was introduced by Al-Odhari. Namely, we speak about families of subsets which contain ∅ and the whole universe X, being at the same time closed under finite intersections (but not necessarily under arbitrary or even finite unions). This slight modification allows us to distinguish between new classes of subsets (infra-open, ps-infra-open and i-genuine). Analogous notions are discussed in the language of closures. The class of minimal infra-open sets is studied too, as well as the idea of generalized infra-spaces. Finally, we obtain characterization of infra-spaces in terms of modal logic, using some of the notions introduced above.

• Proceedings of the Korean Institute of Landscape Architecture Conference
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• 2007.10b
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• pp.49-53
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• 2007

The purpose of this study is to consider the idea and the background of the establishment of master plans for parks and green spaces of metropolis in Japan, China and Korea after a careful comparative review of layout planning of green areas, plan objectives, future images and main measures. The method of study is the analysis of the control and plans in these three countries. The study reveals the characteristic of each plan as follows: 1) the conservation and revitalization of the shape of land and the river system in Tokyo; 2) the materialization of ideal green spaces in Beijing, the combination of the ring green and the radial layout of parks and green spaces; 3) the combination of cruciform greenery and the utilized existing public open spaces in Seoul. The result also shows that these cities have the different development of projects but face the common challenges.

• 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.

• 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.56 no.1
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• pp.301-310
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• 2016

In this paper, we introduce and study the concept of a new class of sets called paraopen sets and paraclosed sets in topological spaces. During this process some of their properties are obtained. Also we introduce and investigate a new class of maps called paracontinuous, *-paracontinuous, parairresolute, minimal paracontinuous and maximal paracontinuous maps and study their basic properties in topological spaces.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.11-17
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• 2011

We study some properties of quasi-topological spaces. Also we introduce the concept of Q-continuity and investigate several types of quasi-topology on an SGNS.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.701-709
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• 2010

We introduce the concepts of IVF irresolute mappings and IVF irresolute open mappings, and investigate characterizations for such mappings on the interval-valued fuzzy topological spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.124-127
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• 2010

In this paper, we introduce the concepts of fuzzy r-minimal continuous function and fuzzy r-minimal open function between a fuzzy r-minimal space and a fuzzy topological space. We also investigate characterizations and properties for such functions.