Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Some Topological Structures of Ordinary Smooth Topological Spaces

  • Lee, Jeong Gon (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Lim, Pyung Ki (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Hur, Kul (Division of Mathematics and Informational Statistics, Wonkwang University)
  • Received : 2012.10.12
  • Accepted : 2012.11.21
  • Published : 2012.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

We introduce the notions of ordinary smooth, quasi-ordinary smooth and weak ordinary smooth structure, showing that various properties of an ordinary smooth topological space can be expressed in terms of these structures. In particular, the definitions and results of [2, 4, 5] may be expressed in terms of the ordinary smooth and quasi-ordinary smooth structures. Furthermore, we present the basic concepts relating to the weak ordinary smooth structure of an ordinary smooth topological space and the fundamental properties of the objects in these structures.

Keywords

Acknowledgement

Supported by : 원광대학교

References

  1. M. S. Cheng, G. B. Chae, K. Hur and S. M. Kim, "The lattice of ordinary smooth topologies," Honam Math. J., vol. 33, no. 4, pp. 453-465, 2011. https://doi.org/10.5831/HMJ.2011.33.4.453
  2. J. G. Lee, P. K. Lim and K. Hur, Closure, interior and compactness in ordinary smooth topological spaces, To be submitted.
  3. J. G. Lee, P. K. Lim and K. Hur, Neighborhood structures of ordinary smooth topological spaces, To be submitted. https://doi.org/10.5831/HMJ.2012.34.4.559
  4. J. G. Lee, P. K. Lim and K. Hur, Closure and interior redefined, and some types of compactness in ordinary smooth topological spaces, To be submitted.
  5. P. K. Lim, B. K. Ryou and K. Hur, "Ordinary smooth topological spaces," IJFIS, vol. 12, no. 1, pp. 66-76, 2012. https://doi.org/10.5391/IJFIS.2012.12.1.66
  6. M. S. Ying, "A new approach for fuzzy topology (I)," Fuzzy Sets and Systems, vol. 39, pp. 303-321, 1991. https://doi.org/10.1016/0165-0114(91)90100-5
  7. M. S. Ying, "A new approach for fuzzy topology (III)," Fuzzy Sets and Systems, vol. 55, pp. 195-207, 1993.