호남수학학술지 (Honam Mathematical Journal)

  • 제33권4호
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  • Pages.453-465
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  • 2011
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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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)
  • 투고 : 2011.08.17
  • 심사 : 2011.09.16
  • 발행 : 2011.12.25
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초록

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.

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참고문헌

  1. C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190. https://doi.org/10.1016/0022-247X(68)90057-7
  2. K.C. Chattopadhyay, R.N. Hazra and S.K. Samanta, Gradation of openness: fuzzy topology, Fuzzy Sets and Systems 49 (1992), 237-242. https://doi.org/10.1016/0165-0114(92)90329-3
  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. https://doi.org/10.1016/0165-0114(93)90277-O
  4. R.N. Hazra, S.K. Samanta and K.C. Chattopadhyay, Fuzzy topology rede ned, Fuzzy Sets and Systems 45 (1992), 79-82. https://doi.org/10.1016/0165-0114(92)90093-J
  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. https://doi.org/10.1016/0022-247X(76)90029-9
  7. W. Peeters, The complete lattice ($\mathbb{S}(X),{\preceq}$) of smooth fuzzy topologies, Fuzzy Sets and Systems 125 (2002), 145-152. https://doi.org/10.1016/S0165-0114(01)00030-6
  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. https://doi.org/10.1016/0022-247X(80)90048-7
  9. A.A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems 48 (1992), 371-375. https://doi.org/10.1016/0165-0114(92)90352-5

피인용 문헌

  1. NEIGHBORHOOD STRUCTURES IN ORDINARY SMOOTH TOPOLOGICAL SPACES vol.34, pp.4, 2012, https://doi.org/10.5831/HMJ.2012.34.4.559
  2. Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces vol.23, pp.1, 2013, https://doi.org/10.5391/JKIIS.2013.23.1.80
  3. Some Topological Structures of Ordinary Smooth Topological Spaces vol.22, pp.6, 2012, https://doi.org/10.5391/JKIIS.2012.22.6.799
  4. Closure, Interior and Compactness in Ordinary Smooth Topological Spaces vol.14, pp.3, 2014, https://doi.org/10.5391/IJFIS.2014.14.3.231