Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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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)
  • Received : 2011.08.17
  • Accepted : 2011.09.16
  • Published : 2011.12.25
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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.

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References

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