• 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.

• East Asian mathematical journal
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• v.21 no.1
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• pp.27-39
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• 2005

We will define p-stack convergence spaces and show that each neighborhood structure is uniquely determined by p-stack convergence structure. Also, we will show that p-stack convergence spaces are a generalization of neighborhood spaces.

• 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.19 no.2
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• pp.197-206
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• 2006

In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated. We introduce quasi-2-normed spaces and quasi-(2; p)-normed spaces, and investigate the properties of quasi-2-normed spaces and quasi-(2; p)-normed spaces.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.87-101
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• 2018

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.137-143
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• 1995

First we recall some properties of the spaces $D_p$ and study the continuity of the operators on $D_p$. We also consider the continuity of the operations on the dual spaces $D'_p$ with the weak topology.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.141-152
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• 2003

In this paper, we define generalized quasi-preclosed sets and gqp-closed functions and obtain some new characterizations of quasi P-normal spaces and quasi P-regular spaces due to Tapi et al. [9,11]. It is shown that the pairwise continuous pre gqp-closed (resp. pairwise preopen pre gqp-closed) surjective image of quasi P-normal (resp. quasi P-regular) space is quasi P-normal (resp. quasi P-regular).

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1043-1052
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• 2011

We introduce a new norm, called the $N^p$-norm (1 $\leq$ p < ${\infty}$ on the space $N^p$(V,W) where V and W are abstract operator spaces. By proving some fundamental properties of the space $N^p$(V,W), we also discover that if W is complete, then the space $N^p$(V,W) is also a Banach space with respect to this norm for 1 $\leq$ p < ${\infty}$.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.695-701
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• 2003

In this paper, we have characterizations of almost P-spaces which are analogous characterizations of P-spaces and we will show that if X is an almost P-space such that it is $C^{*}-embedded$ in every almost P-space in which X is embedded, then $$\mid${\upsilon}X-X$\mid${\leq}1$ and that if $$\mid${\upsilon}X-X$\mid${\leq}1$ and ${\upsilon}X$ is Lindelof, then for any almost P-space Y in which X is dense embedded, then X is $C^{*}-embeded$ in Y.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.939-962
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• 2018

In this paper, we show that the commutator of the intrinsic square function with BMO symbols is bounded on the variable exponent Lebesgue spaces $L^{p({\cdot})}({\mathbb{R}}^n)$ applying a generalization of the classical Rubio de Francia extrapolation. As a consequence we further establish its boundedness on the variable exponent Morrey spaces $\mathcal{M_{p({\cdot}),u}$, Morrey-Herz spaces $M{\dot{K}}^{{\alpha}({\cdot}),{\lambda}}_{q,p({\cdot})}({\mathbb{R}}^n)$ and Herz type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q}_{p({\cdot})}({\mathbb{R}}^n)$, where the exponents ${\alpha}({\cdot})$ and $p({\cdot})$ are variable. Observe that, even when ${\alpha}({\cdot}){\equiv}{\alpha}$ is constant, the corresponding main results are completely new.