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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)
  • 발행 : 2005.03.01

초록

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.

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참고문헌

  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