• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.4
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• pp.512-518
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• 2006

In a strictly two-sided, commutative biquantale, we introduce the notion of ($L,\;{\odot}$)-proximity spaces. We investigate the relations among ($L,\;{\odot}$)-proximity spaces, Hutton ($L,\;{\otimes}$)-uniform spaces, ($L,\;{\odot}$) uniform spaces, enriched ($L,\;{\odot}$)-topological spaces and enriched ($L,\;{\odot}$)-interior spaces.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.919-926
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• 2021

This paper intends to define the metacompact spaces and the D-metacompact spaces as well as study their properties along with their relations with some other topological spaces. Several theoretical results are stated and proved with meticulous care through generalizing many well known theorems concerning with metacompact spaces. These results are supported via handling some illustrative examples.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.121-133
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• 2007

We introduce the notions of (L,M)-neighborhood spaces and (2,M)-fuzzifying neighborhood spaces. We investigate the relations among (L,M)-neighborhood spaces, (L,M)-topological spaces and (2,M)-fuzzifying neighborhood spaces.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.59-65
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• 1996

In this paper, we study spaces admitting cs-semistratification and cs-semistratifications with (CF) property. The class of cs-semistratifiable spaces lies between the class of k-semistratifiable spaces and that of semistratifiable spaces which lie between the class of semi-metric spaces and the class of spaces in which closed sets are $G_{\sigma}$ and really differs from the classes of stratifiable spaces.

• Korean Institute of Interior Design Journal
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• v.20 no.2
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• pp.167-175
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• 2011

This study analyzed the ways of expressing materials to create visual perception spaces in "commercial spaces". The result is as follows. First, it has been discovered that expressing materials in commercial spaces plays an important role in creating various visual perception spaces as well as discriminative spaces, in commercial spaces. Hence, it will be necessary to make a multilateral study on how you can express materials to create visual perception spaces. Second, by referring to earlier studies, four types of space have been deduced as visual perception spaces. These are: "expansion", "central", "borderline" and "decoration" spaces. Third, by considering the space types and characteristics as well as the expressing materials, the criteria for the ways of expressing materials to create visual perception spaces in commercial spaces. Finally, looking at these expression methods, images of "expansion" spaces have most commonly been expressed indistinctly by using the materials and patterns. The profound images of "central" spaces were displayed using the materials and their symbolic images have been shown using the materials and colors. In the "borderline" spaces, the areas have been distinctly segmented or expressed in limited spaces by using the materials and colors. Visual designs were displayed in the "decoration" spaces by using materials from other space fields. All these phenomena have demonstrated that various new materials are being used to create various distinctive designs in commercial spaces. The result of this study shall act as basic reference materials in devising visual designs needed in creating various visual perception spaces.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.397-407
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• 2016

In this paper, the concepts of k-smoothness, k-very smoothness and k-strongly smoothness of Banach spaces are dealt with together briefly by introducing three types k-denting point regarding different topology of conjugate spaces of Banach spaces. In addition, the characterization of first type ${\omega}^*-k$ denting point is described by using the slice of closed unit ball of conjugate spaces.

• East Asian mathematical journal
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• v.23 no.2
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• pp.159-174
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• 2007

In this paper, the concepts of pairwise fuzzy $G_{\delta}$-connected spaces and pairwise fuzzy $G_{\delta}$-extremally disconnected spaces are introduced. The concept of pairwise fuzzy $G_{\delta}$-basically disconnected spaces is defined. Characterizations of the above spaces are given besides giving several examples. Interrelations among the spaces introduced are discussed and some relevant counter examples are given.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.185-199
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• 2020

In this paper, we introduce the definitions of s_p-convergent sequence in fuzzy metric spaces and fuzzy normed spaces. We investigate relations of convergence, s_p-convergence, s_∞-convergence and st-convergence in fuzzy metric spaces and fuzzy normed spaces. We also study s_p-convergence, s_∞-convergence and st-convergence using the sub-sequence of convergent sequence in fuzzy metric spaces and fuzzy normed spaces. Stationary fuzzy normed spaces are defined and investigated. We finally define s_p-closed sets, s_∞-closed sets and st-closed sets in fuzzy metric spaces and fuzzy normed spaces and investigate relations of them.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.129-139
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• 2017

For a map $p:X{\rightarrow}A$, there are concepts of co-$H^p$-spaces, co-$T^p$-spaces, which are generalized ones of co-H-spaces [17,18]. For a principal cofibration $i_r:X{\rightarrow}C_r$ induced by $r:X^{\prime}{\rightarrow}X$ from $\imath:X^{\prime}{\rightarrow}cX^{\prime}$, we obtain some sufficient conditions to having extensions co-$H^{\bar{p}}$-structures and co-$T^{\bar{p}}$-structures on $C_r$ of co-$H^p$-spaces and co-$T^p$-structures on X respectively. We can also obtain some results about co-$H^p$-spaces and co-$T^p$-spaces in homology decompositions for spaces, which are generalizations of Golasinski and Klein's result about co-H-spaces.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.717-723
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• 1997

The compact transformation group has been developed with lots of properties. Many properties which are satisfied on G-space for compact group G do not hold for noncompact case. To recover some theory on spaces with noncompact group action we give some restriction on G-spaces. Hence we introduced Cartan G-spaces and proper G-spaces for our goal and we prove some properties on these G-spaces with noncompact G.