• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.243-252
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• 2018

In this paper, we study the sequentially open and closed subsets of sequential topological groups determined by sequentially continuous group homomorphism. In particular, we investigate the sequentially openness (closedness) and sequentially compactness of subsets of sequential topological groups by the aid of sequentially continuity, sequentially interior or closure operators. Moreover, we explore subgroup and sequential quotient group of a sequential topological group.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.791-801
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• 2005

In this paper, we introduce the concepts of closure and interior defined by an intuitionistic gradation of openness. We also introduce the concepts of weakly gp-maps, gp-open maps and several types of compactness, and obtain some characterizations.

• East Asian mathematical journal
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• v.39 no.1
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• pp.11-21
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• 2023

Non-trivial automorphisms of the unit disc in the complex plane can be classified by three classes; elliptic, parabolic and hyperbolic automorphisms. This classification is due to a representation in the projective special linear group of the real field, or in terms of fixed points on the closure of the unit disc. In this paper, we will characterize this classification by the distance function of the Poincaré metric on the interior of the unit disc.

• Korean Institute of Interior Design Journal
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• no.34
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• pp.106-113
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• 2002

Certosa, a representative Monastic Architecture of Renaissance era, has been well preserved. And it has worked as a symbol of the space form & style revealed by monad, sell, arcade and court, which are characteristic of a monastery. A court is divided into large court and small one, and it connects each units and each sells through the annex with clarifying each space identities. And arcade and pillar is not only to derive a unitary space from entire space, but also to try openness and extension applying a different height in spite of physical closure of style. Especially planned by monad and cell, the routine space of monks, a structure of rational space is a yardstick of moderation and frugality, showing affluent space which occupy essential areas without extra space. And the space appears self-sufficiency, honest poverty, and affluence with order and eternity based on elementary principles of the Cartusio order in composition and plan of the space. Keeping strong linking with entire sells in the monastery, Each sell symbolizes entire sells, and the inverse is the same. And it is the universe advocating eternity and it is also a small city which provides the monks with accurate modules and scales in the very recluse space.

• Korean Institute of Interior Design Journal
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• v.25 no.3
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• pp.3-10
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• 2016

The unexpected expansion of the built environment has allowed for high-density and high-rise buildings. As high-density dwellings compromise privacy, the requirements for balancing between interacting with others and protecting privacy are increasing. In this respect, Korean traditional architecture provides privacy through a proper balance of openness and closure in the courtyard garden. However, it is difficult to analyze privacy quantitatively, as it depends on the individual experience and psychology. The analyzing for visual privacy is a significant issue to resolve a conflict with others and enhance human's comfort. Therefore, this paper addresses the assumption that visual privacy could ultimately be quantified based on the concept of prospect and refuge, one of the design strategies for psychological wellbeing. The purpose of this study is to examine visual privacy in the royal palace in Korea, Gyeongbokgung and Changdeokgung. It measures spatial configuration in each buildings using space syntax, and the area ratio of prospect and refuge through an image analysis with Adobe Photoshop CS6. The mathematical properties of connectivity, depth, control value, integration and the area ratio of prospect and refuge are partially available for quantifying visual privacy in buildings.

• Korean Institute of Interior Design Journal
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• v.18 no.6
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• pp.176-183
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• 2009

This study was intended to define the spatial concept of the boundary structure of the architectural space as well as evaluate the Hyangdan which well represents the features of Korean traditional building in such a way of reviewing the building structure of Korean traditional residential space. The boundary is categorized into visible boundary and invisible boundary which was also functionally classified into the features of isolating, passing, mediating and overlapping. The major elements comprising the boundary structure was analyzed by the characteristic of the pattern so as to define them as the concept of surrounding, duality, hierarchism, continuity and overlapping. Based on such concepts, a boundary structural characteristics of Hyangdan were reevaluated and outlined as follows. The surrounding feature was seen through the outer side of the structure surrounded, two courtyards and eaves, and a duality showing both the closure of main house and openness of detached house was seen through the characteristics of surrounding structure. And the continuous activities toward the inner room and the empty space to link them in a systematic way and repeatedly aligned rooms reveal the overlapping as continuous and transitional space. And finally, an elevated stylobate demonstrates the hierarchical features of the structure.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.230-241
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• 2010

In the present paper we introduce and study fundamental concepts in the framework of L-fuzzifying topology(so called(2,L)-fuzzy topology)as L-concepts where L is a complete residuated lattice. The concepts of (2,L)-derived, (2,L)-closure, (2,L)-interior, (2,L)-exterior and (2,L)-boundary operators are studied and some results on above concepts are obtained. Also, the concepts of an L-convergence of nets and an L-convergence of filters are introduced and some important results are obtained. Furthermore, we introduce and study bases and subbases in (2,L)-topology. As applications of our work the corresponding results(see[10-11]) are generalized and new consequences are obtained.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.1
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• pp.126-134
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• 2012

By using the concept of intuitionistic interval-valued fuzzy sets, we introduce the notion of intuitionistic interval-valued fuzzy topology. And we study some fundamental properties of intuitionistic interval-valued fuzzy topological spaces: First, we obtain analogues[see Theorem 3.11 and 3.12] of neighborhood systems in ordinary topological spaces. Second, we obtain the result[see Theorem 4.9] corresponding to "the 14-set Theorem" in ordinary topological spaces. Finally, we give the initial structure on intuitionistic interval-valued fuzzy topologies[see Theorem 5.9].

• Honam Mathematical Journal
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• v.28 no.3
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• pp.417-431
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• 2006

The notions of IVF strongly semiopen (semiclosed) mappings and IVF strongly semicontinuous mappings are introduced, and several examples are provided. Related properties are investigated. In particular, characterizations of an IVF strongly semiopen mapping and an IVF strongly semicontinuous mapping are discussed.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.93-102
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• 2022

The impact of programming languages in the research sector has helped lot of researchers to broaden their view and extend their work without any limitation. More importantly, even the complex problems can be solved in no matter of time while converting them into a programming language. This convenience provides upper hand for the researchers as it places them in a comfort zone where they can work without much stress. With this context, we have converted the research problems in Topology into programming language with the help of Python. In this paper, we have developed a Python program to find the weaker form of closed sets namely alpha closed set, semi closed set, pre closed set, beta closed set and regular closed set.