International Journal of Fuzzy Logic and Intelligent Systems

  • 제14권3호
  • /
  • Pages.231-239
  • /
  • 2014
  • /
  • 1598-2645(pISSN)
  • /
  • 2093-744X(eISSN)
한국지능시스템학회 (Korean Institute of Intelligent Systems)
권호 표지
DOI QR코드

DOI QR Code

Closure, Interior and Compactness in Ordinary Smooth Topological Spaces

  • Lee, Jeong Gon (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) ;
  • Lim, Pyung Ki (Division of Mathematics and Informational Statistics and Nanoscale Science and Technology Institute, Wonkwang University)
  • 투고 : 2012.09.18
  • 심사 : 2014.06.19
  • 발행 : 2014.09.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

It presents the concepts of ordinary smooth interior and ordinary smooth closure of an ordinary subset and their structural properties. It also introduces the notion of ordinary smooth (open) preserving mapping and addresses some their properties. In addition, it develops the notions of ordinary smooth compactness, ordinary smooth almost compactness, and ordinary near compactness and discusses them in the general framework of ordinary smooth topological spaces.

키워드

참고문헌

  1. R. Badard, "Smooth axiomatics," in Proceedings of the Ist International Fuzzy Systems Association (IFSA) Congress, Palma de Mallorca, Spain, July, 1986.
  2. C. L. Chang, "Fuzzy topological spaces," Journal of Mathematical Analysis and Applications, vol. 24, no. 1, pp. 182-190, Oct. 1968. http://dx.doi.org/10.1016/0022-247X(68)90057-7
  3. R. N. Hazra, S. K. Samanta, and K. C. Chattopadhyay, "Fuzzy topology redefined," Fuzzy Sets and Systems, vol. 45, no. 1, pp. 79-82, Jan. 1992. http://dx.doi.org/10.1016/0165-0114(92)90093-J
  4. K. C. Chattopadhyay, R. N. Hazra, and S. K. Samanta, "Gradation of openness: fuzzy topology," Fuzzy Sets and Systems, vol. 49, no. 2, pp. 237-242, Jul. 1992. http://dx.doi.org/10.1016/0165-0114(92)90329-3
  5. M. Demirci, "Neighborhood structures of smooth topological spaces," Fuzzy Sets and Systems, vol. 92, no. 1, pp. 123-128, Nov. 1997. http://dx.doi.org/10.1016/S0165-0114(96)00132-7
  6. A. A. Ramadan, "Smooth topological spaces," Fuzzy Sets and Systems, vol. 48, no. 3, pp. 371-375, Jun. 1992. http://dx.doi.org/10.1016/0165-0114(92)90352-5
  7. M. K. El Gayyar, E. E. Kerre, and A. A. Ramadan, "Almost compactness and near compactness in smooth topological spaces," Fuzzy Sets and Systems, vol. 62, no. 2, pp. 193-202, Mar. 1994. http://dx.doi.org/10.1016/0165-0114(94)90059-0
  8. M. Ying, "A new approach for fuzzy topology (I)," Fuzzy Sets and Systems, vol. 39, no. 3, pp. 303-321, Feb. 1991. http://dx.doi.org/10.1016/0165-0114(91)90100-5
  9. M. Ying, "A new approach for fuzzy topology (II)," Fuzzy Sets and Systems, vol. 47, no. 2, pp. 221-232, Apr. 1992. http://dx.doi.org/10.1016/0165-0114(92)90181-3
  10. P. K. Lim, B. G. Ryoo, and K. Hur, "Ordinary smooth topological spaces," International Journal of Fuzzy Logic and Intelligent Systems, vol. 12, no. 1, pp. 66-76, Mar. 2012. http://dx.doi.org/10.5391/IJFIS.2012.12.1.66
  11. M. S. Cheong, G. B. Chae, K. Hur, and S. M. Kim, "The lattice of ordinary smooth topologies," Honam Mathematical Journal, vol. 33, no. 4, pp. 453-465, 2011. http://dx.doi.org/10.5831/HMJ.2011.33.4.453