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

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

A. M. Zahran M. Azab Abd-allah A. El-n. G. Abd-rahman

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.

Keywords

Open map , Closed map , Continuous map , Semiopen map , Semiclosed map , Semicontinuous map , 2000 AMS Classification: Primary 54 A 40. Secondary 03E72

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.