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THE LATTICE OF ORDINARY SMOOTH TOPOLOGIES
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  • 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;
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 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
 Cited by
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Some Topological Structures of Ordinary Smooth Topological Spaces,;;;

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2.
NEIGHBORHOOD STRUCTURES IN ORDINARY SMOOTH TOPOLOGICAL SPACES,;;;

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3.
Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces,이정곤;임평기;허걸;

한국지능시스템학회논문지, 2013. vol.23. 1, pp.80-86 crossref(new window)
4.
Closure, Interior and Compactness in Ordinary Smooth Topological Spaces,;;;

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1.
Closure, Interior and Compactness in Ordinary Smooth Topological Spaces, International Journal of Fuzzy Logic and Intelligent Systems, 2014, 14, 3, 231  crossref(new windwow)
2.
Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces, Journal of Korean Institute of Intelligent Systems, 2013, 23, 1, 80  crossref(new windwow)
3.
NEIGHBORHOOD STRUCTURES IN ORDINARY SMOOTH TOPOLOGICAL SPACES, Honam Mathematical Journal, 2012, 34, 4, 559  crossref(new windwow)
4.
Some Topological Structures of Ordinary Smooth Topological Spaces, Journal of Korean Institute of Intelligent Systems, 2012, 22, 6, 799  crossref(new windwow)
 References
1.
C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190. crossref(new window)

2.
K.C. Chattopadhyay, R.N. Hazra and S.K. Samanta, Gradation of openness: fuzzy topology, Fuzzy Sets and Systems 49 (1992), 237-242. crossref(new window)

3.
K.C. Chattopadhyay and S.K. Samanta, Fuzzy topology: Fuzzy closure operator, fuzzy compactness and fuzzy connectedness, Fuzzy Sets and Systems 54 (1993), 207-212. crossref(new window)

4.
R.N. Hazra, S.K. Samanta and K.C. Chattopadhyay, Fuzzy topology rede ned, Fuzzy Sets and Systems 45 (1992), 79-82. crossref(new window)

5.
P. K. Lim, B. K. Ryou and K. Hur, Ordinary smooth topological spaces, to be submitted.

6.
R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math Anal. Appl. 56 (1976), 621-623. crossref(new window)

7.
W. Peeters, The complete lattice ($\mathbb{S}(X),{\preceq}$) of smooth fuzzy topologies, Fuzzy Sets and Systems 125 (2002), 145-152. crossref(new window)

8.
P.M. Pu and Y.M. Liu, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), 571-599. crossref(new window)

9.
A.A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems 48 (1992), 371-375. crossref(new window)