• Korean Journal of Mathematics
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• v.10 no.1
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• pp.59-66
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• 2002

We introduce the ${\kappa}_0$-proximity space as a generalization of the Efremovic-proximity space. We define a product ${\kappa}_0$-proximity and the quotient ${\kappa}_0$-proxmity and show some properties of ${\kappa}_0$-proximity space.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.377-384
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• 2012

In this paper some properties of sequentially closed sets and $k$-closed sets in a topological space are discussed, it is shown that a space is a $k$-quotient image of a metric space if and only if its each sequentially closed set is $k$-closed, and some related examples about connectedness are obtained.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.535-540
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• 2006

In this paper, characterizations of difference quotient transformation in the Krein space which is contained continuously and contractively in the krein space of square summable power series C (z) is obtained from the complementation theory.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1409-1422
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• 2022

A 3-fold quotient terminal singularity is of the type $\frac{1}{r}(b,1,-1)$ with gcd(r, b) = 1. In [6], it is proved that the economic resolution of a 3-fold terminal quotient singularity is isomorphic to a distinguished component of a moduli space 𝓜_𝜃 of 𝜃-stable G-constellations for a suitable 𝜃. This paper proves that each connected component of the moduli space 𝓜_𝜃 has a torus fixed point and classifies all torus fixed points on 𝓜_𝜃. By product, we show that for $\frac{1}{2k+1}(k+1,1,-1)$ case the moduli space 𝓜_𝜃 is irreducible.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.267-280
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• 2023

In this article, we show that the family of all 𝓘^𝒦-open subsets in a topological space forms a topology if 𝒦 is a maximal ideal. We introduce the notion of 𝓘^𝒦-covering map and investigate some basic properties. The notion of quotient map is studied in the context of 𝓘^𝒦-convergence and the relationship between 𝓘^𝒦-continuity and 𝓘^𝒦-quotient map is established. We show that for a maximal ideal 𝒦, the properties of continuity and preserving 𝓘^𝒦-convergence of a function defined on X coincide if and only if X is an 𝓘^𝒦-sequential space.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.532-537
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• 2001

In this paper we introduce the concept of fuzzy quotient spaces as the new ways and investigate their some properties.

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.3
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• pp.94-98
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• 1996

The main goal of this paper is to investigate some properties in close connection with the quotient fuzzy norm $ induced by a fuzzy semi-norm $ on a linear space X and the quotient map $q:X{\rightarrow]X/W, $ where W is a subspace of X.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.332-336
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• 2001

In this paper, we introduce the concept of fuzzy quotient spaces as the new ways and investigate their some properties.

• Korean Institute of Interior Design Journal
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• v.26 no.6
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• pp.116-125
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• 2017

The study is aimed to analyze cases of hotel room designs based on the 'Art Quotient'. It is focused on design elements of livability, analyzing the space design in terms of biophilic design and experiential marketing. This paper proposes a direction for hotel design based on the analysis result. The scope of the study includes the cases of 17 hotels in the area of Seoul achieving five stars in Korea. This paper presents an analysis whether the room space of hotels provide a user-oriented life experience from the perspective of biophilic design and experiential marketing. In this study, we focused on the concept of 'refuge', one of the biophilic design elements that express the value of life sense, and the element of 'sense', one of the strategic experiential modules of experiential marketing. After analyzing the hotel case studies, the space was evaluated using five factors of art quotient as a design method to provide a life experience in the hotel room. Analysis of the design space from the viewpoint of refuge, rather than architectural elements, proved that decorative elements appeared most commonly in all hotel rooms. Further, through an analysis based on the measures of 'sense', an experiential element, visual elements were mostly enforced in among the elements of the five senses. In other words, when designing a hotel room space, visual elements such as color, pattern, furniture, lighting and style are mainly utilized. Examining the analysis of the design elements from the point of view of the art quotient, the rooms of all the hotel's suite types include elements of 'communication'. Most of the hotel rooms focused on stimulating the aesthetic sensibility of customers. This resulted in the elements of 'immersion' showing poor results. In conclusion, it is necessary to provide the five senses of the arts index in a balanced manner to provide a life experience through the five senses.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1233-1242
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• 2009

In 1981 S. A. Saxon and P. P. Narayanaswami ([10]) showed that every (LF)-space has an infinite dimensional separable quotient. In this note we prove that this fails for (LF)$_{tv}$-spaces. We construct a wide class of (LF)$_{tv}$-spaces, which have no infinite dimensional separable quotient.