• 충청수학회지
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• 제26권1호
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• pp.53-69
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• 2013

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.649-664
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• 2021

There have been numerous efforts to provide legal information to the general public easily. Most of the existing legal information services are based on keyword-oriented legal ontology. However, this keyword-oriented ontology construction has a sense of disparity from the relationship between the laws used together in actual cases. To solve this problem, it is necessary to study which laws are actually used together in various judicial precedents. However, this is difficult to implement with the existing methods used in computer science or law. In our study, we analyzed this by using topological data analysis, which has recently attracted attention very promisingly in the field of data analysis. In this paper, we applied the the Mapper algorithm, which is one of the topological data analysis techniques, to visualize the relationships that laws form organically in actual precedents.

• Spatial Information Research
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• 제15권1호
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• pp.35-52
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• 2007

실세계에 가까운 가상현실의 표현기술과 웹을 통해 공간정보를 제공하는 3차원 GIS는 새로이 주목받는 분야 중에 하나이다. 특히, 공간데이터의 상호운용성에 대한 관심이 높아지고 있는 가운데, OGC는 상호운용을 지원하는 공간객체의 위상관계 명세를 발표하였다. 그러나 이 명세서는 2차원 공간객체에 국한되어있다. 이에 본 연구에서는 도시의 경관개선과 GIS 활용 기반 조성의 측면에서 3차원 공간객체의 위상관계를 구축하였다. 나아가 이를 토대로 신도시의 실정에 맞는 경관정보 가시화 방안을 제시하였다. 결과적으로 장소에 구애받지 않고 상시접속이 가능한 현실감 있는 도시경관에 대한 정보공유의 기틀을 마련하였다는 점에서 보다 큰 의의가 있다고 할 것이다.

• 한국실내디자인학회논문집
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• 제13권3호
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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.

• Bulletin of the Korean Chemical Society
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• 제16권2호
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• pp.169-180
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• 1995

A topological theory is introduced to extend Tsenoglou's theory to polymer blends having temporary and permanent networks composed of multicomponent polymers which have miscible and flexible chains. The topological theory may estimate the values of free elastic energy, the molecular weight between entanglements, and the equilibrium shear moduli, and it may establish more correctly the topological relations among these physical quantities. Through such introduction of the topological theory, there can be topologically analyzed the mixing law for the rubbery plateau modulus of a fluid polymer blend, and there can be considered the topological relationship to the equilibrium modulus of an interpenetrating polymer network containing trapped entanglements and dangling segments. The theoretically predictive values are compared and show good agreement with the experimental data for several miscible polymer blends.

• 대한수학회보
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• 제61권1호
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• pp.247-262
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• 2024

In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space X, a syndetically transitive semiflow (T, X, 𝜋) having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a T₃ space X, a transitive, nonminimal semiflow (T, X, 𝜋) having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 Ⅳ
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• pp.2028-2031
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• 2003

This paper proposes a face identification algorithm, robust on lighting condition and complex background. The proposed method estimates facial area under bad light condition by expanding face color boundaries and then finds a lip using the templates for lips. Then the eyes are found using their topological relationship with the long and short axes of lip area. The experimental results have shown that the proposed algorithm is robust on lighting conditions and complex background.

• 호남수학학술지
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• 제33권1호
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• pp.27-41
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• 2011

This paper studies the relationship between L-fuzzy proximities and L-fuzzy topologies by topological fuzzy remote neigh-borhood systems. We will prove that the category of L-fuzzy topo- logical spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a core ective full subcategory.

• 대한수학회지
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• 제49권3호
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• pp.449-473
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• 2012

In the present paper, we study the relationship between continuous order-representability and the fulfillment of the usual covering properties on topological spaces. We also consider the case of some algebraic structures providing an application of our results to the social choice theory context.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.471-481
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• 2024

In this paper, the concept of D-sets will be applied to create D-lindelöf spaces, a new type of topological space covering the property. This is performed by using a D-cover, which is a special type of cover. The primary purpose of this work is to introduce the principles and concepts of D-lindelöf spaces. We look into their properties as well as their relationships with other topological spaces. The basic relationship between D-lindelöf spaces and lindelöf spaces, as well as many other topological spaces, will be given and described, including D-compact, D-countably compact, and D-countably lindelöf spaces. Many novel theories, facts, and illustrative and counter-examples will be investigated. We will use several informative instances to explore certain of the features of the Cartesian product procedure across D-lindelöf spaces as well as additional spaces under more conditions.