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THE LATTICE OF ORDINARY SMOOTH TOPOLOGIES

Cheong, Min-Seok;Chae, Gab-Byung;Hur, Kul;Kim, Sang-Mok

  • Received : 2011.08.17
  • Accepted : 2011.09.16
  • Published : 2011.12.25

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

References

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Cited by

  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

Acknowledgement

Supported by : Wonkwang University