[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5831/HMJ.2011.33.4.453

THE LATTICE OF ORDINARY SMOOTH TOPOLOGIES

Cheong, Min-Seok (Department of Mathematics, Sogang University)
Chae, Gab-Byung (Division of Mathematics and Informational Statistics and Institute of Natural Basic Sciences, Wonkwang University)
Hur, Kul (Division of Mathematics and Informational Statistics and Nanoscale Science and Technology Institute, Wonkwang University)
Kim, Sang-Mok (Division of General Education - Mathematics, Kwangwoon University)

Publication Information

Honam Mathematical Journal / v.33, no.4, 2011 , pp. 453-465 More about this Journal

Abstract

Lim et al. [5] introduce the notion of ordinary smooth topologies by considering the gradation of openness[resp. closedness] of ordinary subsets of X. In this paper, we study a collection of all ordinary smooth topologies on X, say OST(X), in the sense of a lattice. And we prove that OST(X) is a complete lattice.

Keywords

Complete lattice; Ordinary smooth topology; Ordinary smooth cotopology; Ordinary smooth base; Ordinary smooth subbase;

Citations & Related Records

Reference

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3	Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces / [Lee, Jeong Gon;Lim, Pyung Ki;Hur, Kul;] / Journal of the Korean Institute of Intelligent Systems
4	Closure, Interior and Compactness in Ordinary Smooth Topological Spaces / [Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki;] / International Journal of Fuzzy Logic and Intelligent Systems

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1	Jeong Gon Lee. (2013) Journal of Korean Institute of Intelligent Systems Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces / 23 (1) , 80
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3	Jeong Gon Lee. (2014) International Journal of Fuzzy Logic and Intelligent Systems Closure, Interior and Compactness in Ordinary Smooth Topological Spaces / 14 (3) , 231