### A Note on Strongly Lower Semi-Continuous Functions and the Induced Fuzzy Topological Space Generated by Them

#### Abstract

*F*) and the s-induced fuzzy topological space generated by the crisp members of

*F*are examined. In this process, different lower semi-continuities and induced fuzzy spaces generated by them have been defined in a general set up and their few properties have been studied.

#### Keywords

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Chang, C.L., Fuzzy Topological Spaces, J. Math. Anal. Appl., 24, pp. 182-190, 1968.

L.A. Zadeh, Fuzzy Sets, Inform. and control, 8, pp. 338-353, 1965.

R. Lowen, Fuzzy Topological Spaces and Fuzzy Compactness, J. Math. Anal. Appl. 56, pp. 621-633, 1976.

M.D. Weiss, Fixed Points, Separation, and Induced Topologies for Fuzzy Sets, J. Math. Anal. Appl., 50, pp. 142-150, 1975.

Bhaumik, R.N. & Mukherjee, A., Completely Lower Semi-Continuous Functions, Math. Edu. 26, pp. 66-69, 1992.

Mukherjee, A. & Halder, S., -Induced Fuzzy Topological Spaces, Proc. Nat. Sem. on Recent Trends in Maths. & Its Appl., April 28-29, 2003, pp. 177-182, 2003.

Bhaumik, R.N. & Bhattacharya, D., On Regular Semi-Continuous Functions, Math. Edu., xxvi(1), pp. 11-17, 1992.

Bhaumik, R.N. & Mukherjee, A., Some More Results on Completely Induced Fuzzy Topological Spaces, Fuzzy Sets and Systems, 50, pp. 113-117, 1992.

Monsef, M.E. Abd. El. & Ramadan, A.E., On Fuzzy Supra Topological Spaces, Indian J. Pure and Appl. Math., 18, pp. 322-329, 1987.

Mukherjee, A., Some More Results on Induced Fuzzy Topological Spaces, Fuzzy Sets and Systems, 96, pp. 255-258, 1998.

Bhaumik, R.N. & Bhattacharya, D., Regular G-Subsets and Real Compact Spaces, Bull. Cal. Math. Soc., 87, pp. 39-44, 1995.

Dilworth, R.P., The Normal Completion of Lattice of Continuous Functions, Trans. Amer. Math. Soc., 68, pp. 427-438, 1950.

Bhattacharjee, D. & Saha, A.K., Fuzzy Topological Spaces Induced by Regular Lower Semi-Continuous Functions, Proc. Nat. Sem. on Fuzzy Math. & Its Appl., Nov. 25-26, pp. 47-56, 2006.

Saha, A.K. & Bhattacharya, D., A Study on Induced Fuzzy Topological Space Generated By M-RLSC Functions, Proceedings of International Conference on Rough Sets, Fuzzy Sets and Soft Computing, Nov. 5-7, pp. 400-408, 2009.

Alimohammady, M. & Roohi, M., Fuzzy Minimal Structure and Fuzzy Minimal Vector Spaces, Chaos, Solitons and Fractals, 27, pp. 599-605, 2006.

El Naschie, M.S., On The Uncertainty of Cantorian Geometry and The Two-Slit Experiment, Chaos, Solitons and Fractals, 9(3), pp. 517-529, 1998.

El Naschie, M.S., On The Unification of Heterotic Strings, M Theory and E(∞) Theory, Chaos, Solitons and Fractals, 11(14), pp. 2397-2408, 2000.

Kelley, J.L., General Topology, D. Van Nostrand, Princeton, NJ, 1955.

Bhaumik, R.N. & Mukherjee, A., Completely Induced Fuzzy Topological Spaces, Fuzzy Sets and Systems, 47, pp. 387-390, 1992.

Gillman, L. & Jerrison, M., Rings of Continuous Function, Van Nostrand, 1960.

Mack, J.E., Countable Paracompactness and Weak Normality Properties, Trans. Amer. Math. Soc., 148, pp. 256-272, 1970.

Palaniappan, N., Fuzzy Topology, Alpha Science International Ltd; 2002.

Rodabaugh, S.E., Powerset Operator Based Foundation for Point-Set Lattice-Theoretic (Poslat) Fuzzy Set Theories and Topologies, Quaest. Math., 20(3), pp. 463-530, 1997.

Geping, W. & Lanfang, H., On Induced Fuzzy Topological Space, J. Math. Anal. Appl., 108, pp. 495-506, 1985.

Bhattacharya, D. & Saha, A.K., A Note On R-Countably Induced Fuzzy Topological Space, Proc. Nat. Sem. On Rec. Dev. in Math. & Its Appl. Nov. 14-15, pp. 1-5, 2008.

DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2013.45.1.6

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