THE LATTICE OF ORDINARY SMOOTH TOPOLOGIES

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 4,  2011, pp.453-465
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.4.453
Title & Authors
THE LATTICE OF ORDINARY SMOOTH TOPOLOGIES
Cheong, Min-Seok; Chae, Gab-Byung; Hur, Kul; Kim, Sang-Mok;

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;
Language
English
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3.
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4.
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1.
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2.
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3.
NEIGHBORHOOD STRUCTURES IN ORDINARY SMOOTH TOPOLOGICAL SPACES, Honam Mathematical Journal, 2012, 34, 4, 559
4.
Some Topological Structures of Ordinary Smooth Topological Spaces, Journal of Korean Institute of Intelligent Systems, 2012, 22, 6, 799
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