Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

Apu Kumar Saha, Debasish Bhattacharya

Abstract


This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.

Keywords


countable fuzzy topological space; countable fuzzy topological vector space; fuzzy topology

Full Text:

PDF

References


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

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

Das, N.R. & Baishya, P.C., Mixed Fuzzy Topological Spaces, J Fuzzy Math., 3(4), pp. 777-784, 1995.

Tripathy, B.C. & Ray, G.C., On Mixed Fuzzy Topological Spaces and Countability, Soft Computing, 16(10), pp. 1691-1695, 2012.

Tripathy, B.C. & Ray, G.C., Mixed fuzzy ideal topological spaces; Applied Mathematics and Computations, 220, pp. 602-607, 2013.

Tripathy, B.C. & Ray, G.C, On δ-Continuity in Mixed Fuzzy Topological Spaces, Boletim da Sociedade Paranaense de Matemática, 32(2), pp. 175-187, 2014.

Tripathy, B.C. & Ray, G.C, Weakly Continuous Functions on Mixed Fuzzy Topological Spaces; Acta Scientiarum. Technology, 36(2),pp. 331-335, 2014

Bhattacharya, D. & Saha, A.K., Fuzzy Topological Spaces Induced by Regular Lower Semi-Continuous Functions, Proc. Nat. Sem. On Fuzzy Math and 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.

Palaniappan, N., Fuzzy topology. Alpha Science International Ltd., 2002.

Sostak, A.P., On a Fuzzy Topological Structure. Suppl Rend Circ Matem Palermo Ser II, 11, pp. 89-103, 1985.

Ying-Ming, L. & Mao-Kang, L., Fuzzy Topology, World Scientific Publishing Co, 1997.

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

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

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.

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

Lane, E.P., Weak C Insertion of a Continuous Function, Notices, Amer. Math. Soc., 26, A-231, 1979.

Katsaras, A.K. & Liu, D.B., Fuzzy Vector Spaces and Fuzzy Topological Vector Spaces, J. Math. Anal. Appl., 58, pp. 135-146, 1977

Katsaras, A.K., Fuzzy Topological Vector Spaces II. Fuzzy Sets and Systems, 6, pp. 85-95, 1981.




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2015.47.2.4

Refbacks

  • There are currently no refbacks.


View my Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.