• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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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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• v.29 no.4
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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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• v.15 no.1
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• pp.35-52
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• 2007

Three-dimensional GIS, which provides spatial information through expression techniques of virtual reality close to the real world and the web, is one of the fields that attract a new attention. In particular, Open GIS Consortium(OGC) announced a topological relationship specification of spatial object which supports interoperability while interest in interoperability of spatial data is increasing. However, this specification is limited to two-dimensional spatial object. So this research established a topological relationship of three-dimensional spatial object in order to improve urban landscape and provide a foundation to use GIS. Based on this, this study proposes ways to visualize landscape information which is appropriate for new town's circumstances. It can be concluded that this research has a bigger meaning since it established a base of sharing information about realistic urban landscape that can be accessed regardless of place and time.

• 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.

• Bulletin of the Korean Chemical Society
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• v.16 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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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.

• Proceedings of the IEEK Conference
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• 2003.07e
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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.

• Honam Mathematical Journal
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• v.33 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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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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• v.42 no.3
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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.