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Year 2006, Volume: 35 Issue: 2, 161 - 172, 01.02.2006

Abstract

References

  • Chang, C. L. Fuzzy topological spces, J. Math. Anal. Appl. 24, 182–190, 1968.
  • Chattopadhyay, K. C., Hazra, R. N. and Sammanta, S. K. Fuzzy topology redefined, Fuzzy Sets and Systems 45, 49–82, 1992.
  • Chattopadhyay, K. C., Hazra, R. N. and Sammanta, S. K. Gradation of openness: fuzzy topology, Fuzzy Sets and Systems 49, 237–242, 1992.
  • Chattopadhyay, K. C. and Sammanta, S. K. Fuzzy topology: fuzzy closure operator, fuzzy compactness, fuzzy connectdeness, Fuzzy Sets and Systems 54, 207–212, 1993.
  • El Gayyar, M. K., Kerre, E. E. and Ramadan, A. A. Almost compactness and near compact- ness in smooth topological spaces, Fuzzy Sets and Systems 62, 193–202, 1994.
  • Ghanim, M. H. and Hasan, H. M. L-closure spaces, Fuzzy sets and systems 33, 154–170, 1989.
  • Ghanim, M. H. and Mashhour, A. M. Fuzzy closure spaces, J. Math. Anal. Appl. 106, 154– 170, 1985.
  • Goguen, J. A. The fuzzy Tychonoff theoem, J. Math. Anal. Appl. 43, 734–742, 1973.
  • Kim, Y. C. Smooth fuzzy closure and topological spaces, Kangweon-Kyungki Math. Jour. 7(1), 11–25, 1999.
  • Kim, Y. C. Initial L-fuzzy closure spaces, Fuzzy Sets and Systems 133, 277–297, 2003.
  • Klien, A. Geneating fuzzy topologies with semi-closue operators, Fuzzy Sets and Systems 9, 267–274, 1983.
  • Ramadan, A. A. Smooth topological spaces, Fuzzy Sets and Systems 48, 371–375, 1992.
  • ˇSostak, A. P. On fuzzy topological structures, Rend. Cire. Matem. Palerma ser. II 11, 89–103, 1985.
  • ˇSostak, A. P. Two decades of fuzzy topology: basic ideas, notions and results, Russian Math.
  • Suveys, 44 (6), 125–186, 1989.
  • ˇSostak, A. P. Basic structures of fuzzy topology, J. Math. Sci. 78 (6), 662–701, 1996.

Notions of Openness and Closedness for Maps between L-Fuzzy Closure Spaces

Year 2006, Volume: 35 Issue: 2, 161 - 172, 01.02.2006

Abstract

In this paper the authors introduce and characterize r-open, r-semiopen sets (resp. r-closed, r-semiclosed sets) and open, semiopen and semicontinuous maps (resp. closed, semiclosed maps) in L-fuzzy closure spaces.

References

  • Chang, C. L. Fuzzy topological spces, J. Math. Anal. Appl. 24, 182–190, 1968.
  • Chattopadhyay, K. C., Hazra, R. N. and Sammanta, S. K. Fuzzy topology redefined, Fuzzy Sets and Systems 45, 49–82, 1992.
  • Chattopadhyay, K. C., Hazra, R. N. and Sammanta, S. K. Gradation of openness: fuzzy topology, Fuzzy Sets and Systems 49, 237–242, 1992.
  • Chattopadhyay, K. C. and Sammanta, S. K. Fuzzy topology: fuzzy closure operator, fuzzy compactness, fuzzy connectdeness, Fuzzy Sets and Systems 54, 207–212, 1993.
  • El Gayyar, M. K., Kerre, E. E. and Ramadan, A. A. Almost compactness and near compact- ness in smooth topological spaces, Fuzzy Sets and Systems 62, 193–202, 1994.
  • Ghanim, M. H. and Hasan, H. M. L-closure spaces, Fuzzy sets and systems 33, 154–170, 1989.
  • Ghanim, M. H. and Mashhour, A. M. Fuzzy closure spaces, J. Math. Anal. Appl. 106, 154– 170, 1985.
  • Goguen, J. A. The fuzzy Tychonoff theoem, J. Math. Anal. Appl. 43, 734–742, 1973.
  • Kim, Y. C. Smooth fuzzy closure and topological spaces, Kangweon-Kyungki Math. Jour. 7(1), 11–25, 1999.
  • Kim, Y. C. Initial L-fuzzy closure spaces, Fuzzy Sets and Systems 133, 277–297, 2003.
  • Klien, A. Geneating fuzzy topologies with semi-closue operators, Fuzzy Sets and Systems 9, 267–274, 1983.
  • Ramadan, A. A. Smooth topological spaces, Fuzzy Sets and Systems 48, 371–375, 1992.
  • ˇSostak, A. P. On fuzzy topological structures, Rend. Cire. Matem. Palerma ser. II 11, 89–103, 1985.
  • ˇSostak, A. P. Two decades of fuzzy topology: basic ideas, notions and results, Russian Math.
  • Suveys, 44 (6), 125–186, 1989.
  • ˇSostak, A. P. Basic structures of fuzzy topology, J. Math. Sci. 78 (6), 662–701, 1996.
There are 16 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

A. M. Zahran This is me

M. Azab Abd-allah This is me

A. El-n. G. Abd-rahman This is me

Publication Date February 1, 2006
Published in Issue Year 2006 Volume: 35 Issue: 2

Cite

APA Zahran, A. M., Abd-allah, M. A., & Abd-rahman, A. E.-n. G. (2006). Notions of Openness and Closedness for Maps between L-Fuzzy Closure Spaces. Hacettepe Journal of Mathematics and Statistics, 35(2), 161-172.
AMA Zahran AM, Abd-allah MA, Abd-rahman AEnG. Notions of Openness and Closedness for Maps between L-Fuzzy Closure Spaces. Hacettepe Journal of Mathematics and Statistics. February 2006;35(2):161-172.
Chicago Zahran, A. M., M. Azab Abd-allah, and A. El-n. G. Abd-rahman. “Notions of Openness and Closedness for Maps Between L-Fuzzy Closure Spaces”. Hacettepe Journal of Mathematics and Statistics 35, no. 2 (February 2006): 161-72.
EndNote Zahran AM, Abd-allah MA, Abd-rahman AE-nG (February 1, 2006) Notions of Openness and Closedness for Maps between L-Fuzzy Closure Spaces. Hacettepe Journal of Mathematics and Statistics 35 2 161–172.
IEEE A. M. Zahran, M. A. Abd-allah, and A. E.-n. G. Abd-rahman, “Notions of Openness and Closedness for Maps between L-Fuzzy Closure Spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 35, no. 2, pp. 161–172, 2006.
ISNAD Zahran, A. M. et al. “Notions of Openness and Closedness for Maps Between L-Fuzzy Closure Spaces”. Hacettepe Journal of Mathematics and Statistics 35/2 (February 2006), 161-172.
JAMA Zahran AM, Abd-allah MA, Abd-rahman AE-nG. Notions of Openness and Closedness for Maps between L-Fuzzy Closure Spaces. Hacettepe Journal of Mathematics and Statistics. 2006;35:161–172.
MLA Zahran, A. M. et al. “Notions of Openness and Closedness for Maps Between L-Fuzzy Closure Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 35, no. 2, 2006, pp. 161-72.
Vancouver Zahran AM, Abd-allah MA, Abd-rahman AE-nG. Notions of Openness and Closedness for Maps between L-Fuzzy Closure Spaces. Hacettepe Journal of Mathematics and Statistics. 2006;35(2):161-72.