• 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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1391-1408
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• 2023

Let M and M^# be Hardy-Littlewood maximal operator and sharp maximal operator, respectively. In this article, we present necessary and sufficient conditions for the boundedness properties for commutator operators [M, b] and [M^#, b] in a general context of Banach function spaces when b belongs to BMO(?ⁿ) spaces. Some applications of the results on weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces and Musielak-Orlicz spaces are also given.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.351-359
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• 2019

In this paper, we introduce a modification of extremally disconnected spaces which is said to be m-extremally disconnected. And we obtain many characterizations of m-extremally disconnected spaces. The concepts of ${\ast}$-extremally disconnected spaces, ${\ast}$-hyperconnected spaces, and generalized hyperconnectedness are as examples for this paper.

• Korean Institute of Interior Design Journal
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• v.26 no.4
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• pp.57-64
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• 2017

Modern Christian spaces are developing from the past architectural styles to the phenomenological aspects. This study was conducted since it was judged that research and analysis is desirable with the application of religious phenomenological theories which fit the characteristics of religious spaces. A scholar of religion, M. Eliade studied religious phenomenology based on religious studies. This study analyzed the characteristics of religious phenomenology of the Christian spaces based on his theory. As a research method, this study analyzed the category of religious studies and religious phenomenology derived from them and selected M. Eliade as one of the theorists in the field of religious phenomenology. Study drew out the characteristics of Christian spaces from the perspective of M. Eliade's religious phenomenology as follows; In the Christian spaces, characteristics of experiential spatiality and ambiguous spatiality appeared in relation to the spaces of 'Sacred' and 'Profane' which M. Eliade aimed to explain. The characteristics of Christian spaces drawn out from the time of 'Sacred' and 'Profane', which is M. Eliade's theory, were fundamental temporality, environmental temporality and subjective temporality. From the structure and form of 'Sacred' and 'Profane', which is M. Eliade's theory, the characteristics of Christian spaces can be considered to be formative symbolism and physical naturalness. Various characteristics of Christian spaces materialize the concepts of 'hierophany' and 'sublimity' vaguely felt in religious spaces. The results of this study is expected to provide researchers, religious people and general public who study Christian spaces with research basis to further objectify results of their studies as well as basic data on the phenomenological methodology of religion.

• 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.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.73-86
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• 2014

In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.

• East Asian mathematical journal
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• v.25 no.2
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• pp.197-213
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• 2009

In this paper, we give some new denitions of $\cal{L}^*_\cal{M}$-fuzzy metric spaces and we prove a common xed point theorem for two mappings in complete $\cal{L}^*_\cal{M}$-fuzzy metric spaces. We get some improved versions of several xed point theorems in complete $\cal{L}^*_\cal{M}$-fuzzy metric spaces.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.289-308
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• 2022

In this paper, we introduce the concept of M^*-metric spaces and how much the M^*-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M^*-metric spaces. Also, we investigate some types of convergence associated with M^*-metric spaces. Some common fixed point for contraction and generalized contraction mappings in M^*-metric spaces. Our work has been supported by many examples and an application.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.727-737
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• 2009

Let M(X) be the space of all pointwise multipliers of Banach space X. We will show that, for each $\alpha>1$, $M(\mathfrak{B}_\alpha)=M(\mathfrak{B}_{\alpha,0})=H^\infty{(B)}$. We will also show that, for each $0<{\alpha}<1$, $M(\mathfrak{B}_\alpha)$ and $M(\mathfrak{B}_{\alpha,0})$ are Banach algebras. It is established that certain inclusion relationships exist between the weighted Bloch spaces and holomorphic Besov spaces.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.525-540
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• 2023

In this paper, we introduce the concept of fuzzy nano M open and fuzzy nano M closed mappings in fuzzy nano topological spaces. Also, we study about fuzzy nano M Homeomorphism, almost fuzzy nano M totally mappings, almost fuzzy nano M totally continuous mappings and super fuzzy nano M clopen continuous functions and their properties in fuzzy nano topological spaces. By using these mappings, we can able to extended the relation between normal spaces and regular spaces in fuzzy nano topological spaces.