• Honam Mathematical Journal
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• v.33 no.4
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• pp.617-628
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• 2011

In relation to the classification of finite topological spaces the paper [17] studied various properties of finite topological spaces. Indeed, the study of future internet system can be very related to that of locally finite topological spaces with some order structures such as preorder, partial order, pretopology, Alexandroff topological structure and so forth. The paper generalizes the results from [17] so that the paper can enlarge topological and homotopic properties suggested in the category of finite topological spaces into those in the category of locally finite topological spaces including ALF spaces.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.697-705
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• 2023

We studied new notions of analogues of topological rings. Salih [10] acquaints us with the notion of irresolute topological ring in 2018. In this paper, we further studied the space closely and characterized indispensable properties of the space. We prove that every open subset of an irresolute topological ring is irresolute topological ring. We also obtained the equivalent condition of neighborhood of an element in an irresolute topological ring. It is proved that ring homeomorphism of an irresolute topological ring is irresolute if it is irresolute at identity element e in the irresolute topological ring 𝓡.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.3
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• pp.88-94
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• 1998

We will difine a base of a smooth fuzzy topological space and investigate some properties of bases. We will prove the existences of initial smooth fuzzy topological spaces. From this fact, we can define subspaces and products of smooth fuzzy topological spaces.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.409-415
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• 2011

We introduce the notion of weakly quasi generalized continuous functions, and investigate properties for the continuity.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.173-178
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• 1996

In this paper, we discuss quasi-fuzzy H-closed space and introduce ${\theta}$-convergence of prefilter in fuzzy topological space. And we define ${\theta}$-closed fuzzy set using by ${\theta}$-convergence.

• Korean Institute of Interior Design Journal
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• v.13 no.3
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• pp.69-75
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• 2004

Since 1990s, several rising western architects have been moving their theoretical background from the modern paradigm to new science and philosophy. Architectural spaces are based on the philosophy and science of their own age and the architectural theories made by them. And specially, it seems that topological spaces are different to theoretical backgrounds from idealized spaces of modern architecture. From these backgrounds, this study was performed to search for the spacial relationship and characteristics shown in the recently folding architecture and the results of this study that starts this purpose are as follows. First, the architecture that introduced by the theory of topology has appeared as the circulation forms like as Mobius band or Klein bottle, and was made the space fused with structure pursuing liquid properties of matter. As follows, second, the concept of topological space made the division of traditional concept of floor, wall, ceiling disappeared and had built up the space by continual transformation. Third, about the relationship between two spaces in topological space, the two spaces were happened by transformation of these and they have always continuity and the same quality.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.647-673
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• 2002

There are many models to study topological $R^2$-planes. Unlike topological $R^2$-planes, it is difficult to find models to study topological R$^3$)-spaces. If an 4-dimensional affine plane intersects with R$^3$, we are able to get a geometrical structure on R$^3$ which is similar to R$^3$-space, and called $R^2$-divisible R$^3$-space. Such spatial geometric models is useful to study topological R$^3$-spaces. Hence, we introduce some classes of topological $R^2$-divisible R$^3$-spaces which are induced from 4-dimensional anne planes.

• Korean Institute of Interior Design Journal
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• v.14 no.3 s.50
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• pp.64-72
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• 2005

The purpose of this study is to propose a topological design principles and to analyze the space of digital architecture applying topological invariant expressive characteristics. As this study is based on topology as a science of true world's pattern, we intented to explain the concepts and provide some methods of low-level and hyperspace topological invariant Properties. Four major aspects are discussed. Those are connection theory, boundary concept, homotopy group, knot Pattern theory as topological invariant properties. Then we intented to make understand topological characteristics of the Algorithms, luring machine, cellular automata, string theory, membrane, DNA and supramolecular chemistry. In fine, the topological invariant properties of the digital architecture as genetic algorithms based on self-organization and heterogeneous networks of interacting actors can be analyzed and used as a critical tool. Therefore topology can be provided endless possibilities for architecture, designers and scientists intended in expressing the more complex and organic patterns of nature as life.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.221-236
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• 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces and then these are used to generalize the notions of interior and closure. Further, we study the properties of semiopen soft sets, semiclosed soft sets, semi interior and semi closure of soft set in soft topological spaces. Various forms of soft functions, like semicontinuous, irresolute, semiopen and semiclosed soft functions are introduced and characterized including those of soft semicompactness, soft semiconnectedness. Besides, soft semiseparation axioms are also introduced and studied.

• Honam Mathematical Journal
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• v.26 no.2
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• pp.163-192
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• 2004

In this paper, we introduce the concepts of intuitionistic fuzzy subspaces, intuitionistic fuzzy topological groups and intuitionistic fuzzy quotient groups. And we investigate some of their properties.