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孔在應 건국대학교 교육대학원 1987 敎育論叢 Vol.7 No.-
A uniform structure on a set X was first defined by Weil in terms of subsets of X×X, in 1937. Tukey later defined a uniform structure on X in terms of families of covers of X. In this paper, we study questions concerning the relationship between uniform structures and proximity structures, and we obtain the fact that proximity structures lie between topological structures and uniform structures.
孔在應 建國大學校 敎育硏究所 1977 論文集 Vol.2 No.-
The radical concept on a commutative ring R with identity is viewed as vital in the structure theory. In this article, I treated the structure of the radicals of a commutative ring R with identity. Through the paper, we may obtain the facts that the Jacobson radical rad (R/rad R) of the factor ring R/rad R by the Jacobson radical rad R is semiprimitive and the prime radical Rad(R/Rad) of the factor ring R/Rad R by the prime radical Rad R is semiprime.
孔在應 建國大學校 敎育硏究所 1978 論文集 Vol.3 No.-
Suppose that Ⅱis any set of prime ideals of a commutative ring R with identity In this article, we will find how to introduce a topological structure on the set Ⅱand ob-tain some properties of the prime ideal space Ⅱ.
孔在應 建國大學校 敎育硏究所 1992 論文集 Vol.16 No.-
Nearness structures have been defined as a means of unifying various topological concepts. In this paper we show that the collection of all nearness structures on a set X forms a complete lattice and give necessary and sufficient conditions for a nearness space to be metrizable.
孔在應 건국대학교 1985 學術誌 Vol.29 No.2
In 1952, V. A. Efremovicˇ introduced a concept of nearness between two sets yielding proximity. Then the concept of proximity was axiomatized by several mathematicians. In this paper, we examine some results in the theory of the LO-Proximity structures using clusters.
孔在應 건국대학교 교육대학원 1983 敎育論叢 Vol.3 No.-
There are traces of the concept of filters as early as 1914 in Root's article. Filters were introduced in 1937 by Cartan. Bourbaki employed them in their text in 1940. In this same year, Tukey studied nets and filters. The equivalence between filters and nets was first discussed in 1955 by Bartle. The most complete reliance on filters for the development of topology can be found in Kowalsky (1961). In this note, we obtain the fact that collection Φ^*(X) consisting of all filters on X and the null filter on X forms a complete distributive lattice.
孔在應 건국대학교 1981 學術誌 Vol.25 No.1
The concepts of the inverse limit play an important role in modern topologies, in particular, Cˇech homology theories. In this paper, we use the concept of a kind of the inverse limit to define the Cˇech homology groups and study some properties associated with them.
First Countable CDH공간의 Components에 관하여
공재응 ( Jai Eung Kong ),조성기 ( Sung Ki Cho ) 건국대학교 교육연구소 1994 교사와 교육(구 교육논집) Vol.18 No.-
B. Fitzpatrick Jr와 N.F. Lauer 등은 CDH 공간의 nondegenerate component들이 open CDH 공간이 된다는 것과 connected CDH 공간이 homogeneous가 된다는 것을 독립적으로 증명하였다. 본 연구에서는 CDH 공간이 first countable인 경우 이러한 사실 들은 이 공간이 갖고 있는 하나의 성질의 결과들임을 보였다.