• 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.

• 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.

• 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.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.177-186
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• 2016

For a map $f:A{\rightarrow}X$, there are concepts of $H^f$-spaces, $T^f$-spaces, which are generalized ones of H-spaces [17,18]. In general, Any H-space is an $H^f$-space, any $H^f$-space is a $T^f$-space. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain some sufficient conditions to having liftings $H^{\bar{f}}$-structures and $T^{\bar{f}}$-structures on $E_k$ of $H^f$-structures and $T^f$-structures on X respectively. We can also obtain some results about $H^f$-spaces and $T^f$-spaces in Postnikov systems for spaces, which are generalizations of Kahn's result about H-spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.4
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• pp.514-519
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• 2005

We define extensional spaces. Moreover, we investigate the relations among T-upper-approximation spaces, T-quasi -equivalence relations and extensional spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.1
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• pp.83-88
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• 2002

We study some properties of smooth uniform spaces. We investigate the relationship between smooth topological spaces and smooth uniform spaces. In particular, we define a subspace of a smooth uniform space and a product of smooth uniform spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.2
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• pp.252-257
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• 2006

In strictly two-sided, commutative biquantale, we show that Hutton (L, $\otimes$)-uniform spaces and (L, $\odot$)-uniform spaces induce enriched (L, $\odot$)-topological spaces and enriched (L, $\odot$)-interior 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.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.567-578
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• 2017

Many scholars studied the boundedness of $Ces{\grave{a}}ro$ operators between $Q_K$ spaces and Bloch spaces of holomorphic functions in the unit disc in the complex plane, however, they did not describe the compactness. Let 0 < ${\alpha}$ < $+{\infty}$, K(r) be right continuous nondecreasing functions on (0, $+{\infty}$) and satisfy $${\displaystyle\smashmargin{2}{\int\nolimits_0}^{\frac{1}{e}}}K({\log}{\frac{1}{r}})rdr<+{\infty}$$. Suppose g is a holomorphic function in the unit disk. In this paper, some sufficient and necessary conditions for the extended $Ces{\grave{a}}ro$ operators $T_g$ between ${\alpha}$-Bloch spaces and $Q_K$ spaces in the unit disc to be bounded and compact are obtained.