DOI QR코드

DOI QR Code

On the goodness of some types of fuzzy paracompactness in Sostak's fuzzy topology

  • Kim, Yong-Chan (Department of Mathematics, Kangnung National University) ;
  • Abbas, S.E. (Department of Mathematics, Faculty of Science)
  • Published : 2005.03.01

Abstract

We introduce in Sostak's fuzzy topological spaces definitions of paracompactness, almost paracompactness, and near paracompactness all of which turn to be good extensions of their classical topological counterparts. Fuzzy semi-paracompact, para S-closed and weakly paracompact spaces are treated to a similar approach.

Keywords

References

  1. H. Aygun, M. W. Warner and S. R. T. Kudri 'On smooth L-fuzzy topological spaces' J. Fuzzy Math. vol. 5(2) 1997,pp 321-338, 1997
  2. A. Bulbul and M. W. Warner, 'On the goodness of some types of fuzzy paracompactness' Fuzzy Sets and Systems, vol 55, pp.187-191, 1993 https://doi.org/10.1016/0165-0114(93)90131-Z
  3. C. L. Chang, 'Fuzzy topological spaces', J. Math. Anal. Appl., vol 24, pp.182-190, 1968 https://doi.org/10.1016/0022-247X(68)90057-7
  4. K. C. Chattopadhyay and S. K. Samanta,'Fuzzy topology: fuzzy closure operator, fuzzy compactness and fuzzy connectedness', Fuzzy Sets and Systems, vol 54, pp.207-212, 1993 https://doi.org/10.1016/0165-0114(93)90277-O
  5. K. C. Chattopadhyay, S. N. Hazra, S. K. Samanta, 'Gradation of openness: fuzzy topology', Fuzzy Sets and Systems, vol 49, pp. 237-242, 1992 https://doi.org/10.1016/0165-0114(92)90329-3
  6. M. Demirci, 'On several types of compactness in smooth topological spaces' Fuzzy Sets and Systems, vol 90(1), pp. 83-88, 1997 https://doi.org/10.1016/S0165-0114(96)00121-2
  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, pp. 193-202, 1994 https://doi.org/10.1016/0165-0114(94)90059-0
  8. U. Hoehle and A. P. Sostak, 'A general theory of fuzzy topological spaces', Fuzzy Sets and Systems, vol 73, pp. 131-149, 1995 https://doi.org/10.1016/0165-0114(94)00368-H
  9. U. Hoehle and A. P. Sostak, 'Axiomatic Foundations of Fixed-Basis fuzzy topology', The Handbooks of Fuzzy sets series, Volume 3, Kluwer Academic Publishers, Dordrecht (Chapter 3) 1999
  10. T. Kubiak and A. P. Sostak,'Lower set-valued fuzzy topologies,' Quaestiones Mathematicae, vol 20 pp. 423-429, 1997 https://doi.org/10.1080/16073606.1997.9632016
  11. R. Lowen, 'Fuzzy topological spaces and fuzzy compactness', J. Math. Anal. Appl. vol 56 pp. 621-633, 1976 https://doi.org/10.1016/0022-247X(76)90029-9
  12. A. A. Ramadan, 'Smooth topological spaces', Fuzzy Sets and Systems, vol 48, pp. 371-375, 1992 https://doi.org/10.1016/0165-0114(92)90352-5
  13. A. A. Ramadan, 'On smooth topological spaces III' J. Fuzzy Math. vol 8(1), pp.35-64, 2000
  14. A. A. Ramadan and S. E. Abbas,'On L-smooth paracompactness'J. Fuzzy Math., vol 9(2) 2001
  15. A. A. Ramadan, S. E. Abbas and Yong Chan Kim, 'Almost paracompactness and near paracompactness in L-smooth topological spaces', J. Korea Fuzzy Logic and Intelligent Systems, vol 10(6), pp.564-568, 2000
  16. A. P. Sostak, 'On a fuzzy topological structure,' Suppl. Rend. Circ. Matern. Palerms ser II, vol 11, pp. 89-103, 1985
  17. A. P. Sostak, 'On the neighbourhood structure of a fuzzy topological space,' Zb. Rodova Univ. Nis, ser Math, vol 4, pp. 7-14, 1990
  18. A. P. Sostak, 'Basic structures of fuzzy topology', J. of Math. Sciences, vol 78, No 6, pp. 662-701, 1996 https://doi.org/10.1007/BF02363065