한국지능시스템학회논문지 (Journal of the Korean Institute of Intelligent Systems)

  • 제23권1호
  • /
  • Pages.80-86
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  • 2013
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  • 1976-9172(pISSN)
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  • 2288-2324(eISSN)
한국지능시스템학회 (Korean Institute of Intelligent Systems)
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Closures and Interiors Redefined, and Some Types of Compactness in Ordinary Smooth Topological Spaces

  • Lee, Jeong Gon (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Lim, Pyung Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
  • 투고 : 2012.09.27
  • 심사 : 2012.12.18
  • 발행 : 2013.02.25
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초록

We give a new definition of ordinary smooth closure and ordinary smooth interior of an ordinary subset in an ordinary smooth topological space which have almost all the properties of the corresponding operators in a classical topological space. As a consequence of these definitions we reduce the additional hypotheses in the results of [1] and also generalize several properties of the types of compactness in [1].

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참고문헌

  1. J. G. Lee, K. Hur and P. K. Lim, Closure, Interior and Compactness in Ordinary Smooth Topological Spaces, To be submitted.
  2. A. P. Sostak, On a Fuzzy Topological Structure, Rend. Circ. Matem. Palermo (2) Suppl. 11(1985), 89-103.
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  6. M. El-Dardery, Y. C. Kim and A. A. Ramadan, Smooth Uniform Spaces, IJFIS. 2(1)(2002), 90-95.
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  9. P. K. Lim, B. K. Ryou and K. Hur, Ordinary Smooth Topological Spaces, IJFIS. 12(1)(2012), 66-76. https://doi.org/10.5391/IJFIS.2012.12.1.66
  10. M. S. Cheong, G. B. Chae, K. Hur and S. M. Kim, The Lattice of Ordinary Smooth Topologies, Honam Math. J. 33(4)(2011), 453-465. https://doi.org/10.5831/HMJ.2011.33.4.453
  11. M. Ying, A New Approach for Fuzzy Topology (III), Fuzzy Sets and Systems 55(1933), 195-207.