• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.847-854
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• 1998

We investigate categorical properties of the category NFrm of nearness frames and uniform homomorphisms. We introduce a concept of weakly strong nearness frames and study its permanence properties.

• Journal of Advanced Navigation Technology
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• v.10 no.2
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• pp.145-151
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• 2006

In this paper, we propose a novel navigation method combined Nearness Diagram, Limit-Cycle method and the Vector Field Method for avoidance of unexpected obstacles in the dynamic environment. The Limit-Cycle method is used to obstacle avoidance in front of the robot and the Vector Field Method is used to obstacle avoidance in the side of robot. And the Nearness Diagram Navigation is used to obstacle avoidance in the nearness area of the robot. The performance of the proposed method is demonstrate by simulations.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.175-182
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• 2008

This paper is a revised version of [5]. In [5], we define' nearness between two points' in a topological space in many ways and show that a continuous function preserves one-sided nearness. We also show that a $T_1$-space is characterized by one-sided nearness exactly. In this paper, we introduce extremally disconnected spaces and show that the new topology generated by the set of equivalence classes as a base is extremally disconnected.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.19-27
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• 1995

In 1974 H.Herrlich invented nearness spaces, a very fruitful concept which enables one to unify topological aspects. In this paper, we introduce the Lindel$\ddot{o}$f nearness structure, countably bounded nearness structure and countably totally bounded nearness structure. And we show that (X, ${\xi}_L$) is concrete and complete if and only if ${\xi}_L={\xi}_t$ in a symmetric topological space (X, t). Also we show that the following are equivalent in a symmetric topological space (X, t): (1) (X, ${\xi}_L$) is countably totally bounded. (2) (X, ${\xi}_t$) is countably totally bounded. (3) (X, t) is countably compact.

• East Asian mathematical journal
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• v.35 no.2
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• pp.239-257
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• 2019

The purpose of this study is to show that the topology is closely related to some subjects learned in school mathematics and then to give motivations for learning of the topology. To do this, it is showed that the topology is an abstracted device that deal with structure of limit and continuity introduced in school mathematics. This study took a literature study. The results of this study are as follows. First, the formal definition of general topology to structure open sets was examined. The nearness relation together with the closure operation was introduced and used to characterize for construction of general topology. Second, as definitions for continuity of function, we considered the intuitive definition, definition, structured definitions using open intervals and definition using open sets and then we investigated their roles. We also examined equivalent definition using the nearness relation which is helpful to understand continuity of function. Third, the sequence and its limit are treated in terms of continuous functions having the set of natural numbers and its extended set as domains. From these, it can be concluded that the convergence of sequence and the continuity of function are identified as functions that preserve the nearness relation and that the topology is a specialized tool for dealing with convergence and continuity.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.229-235
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• 2002

A generalized Stein-rule estimator of the vector of regression coefficients in linear regression model is considered and its properties are analyzed according to the criterion of Pitman nearness. A comparative study shows that the generalized Stein-rule estimator representing a class of estimators contains particular members which are better than the usual Stein-rule estimator according to the Pitman closeness.

• Korean Journal of Mathematics
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• v.3 no.2
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• pp.249-257
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• 1995

• Kyungpook Mathematical Journal
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• v.23 no.1
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• pp.49-61
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• 1983

• East Asian mathematical journal
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• v.2
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• pp.45-51
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• 1986

• Proceedings of the Korean Society for History of Mathematics Conference
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• 1998.11a
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• pp.3-3
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• 1998