New Maps in Fuzzy Topological Spaces

Abstract

In this paper, we introduce fuzzy sgw-open and fuzzy sgw-closed maps in fts and obtain certain characterization of the sgw- closed and sgw-open maps. 2010 Mathematics Subject Classification: 54A40

Introduction

I. INTRODUCTION

The concept of a fuzzy subset was introduced and studied by L.A.Zadeh  in the year 1965. The subsequent research activities in this area and related areas have found applications in many branches of science and engineering. In the year 1965, L.A.Zadeh [1] introduced the concept of  fuzzy subset as a generalization of that of an ordinary subset. The introduction of fuzzy subsets paved the way for rapid research work in many areas of mathematical science. In the year 1968, C.L.Chang [2] introduced the concept of fuzzy topological spaces as an application of fuzzy sets to topological spaces . Subsequently several researchers contributed to the development of the theory and applications of fuzzy topology. The theory of fuzzy topological spaces can be regarded as a generalization theory of  topological spaces. An ordinary subset A or a set X can be characterized by a function called characteristic function 

References

[1] L.A.Zadeh, Fuzzy sets, Information and control, 8 (1965) 338-353. [2] C.L.Chang,Fuzzy topological spaces, JI. Math. Anal. Appl., 24(1968), 182-190. [3] K.K.Azad,On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity. JI. Math. Anal. Appl. 82 No. 1 (1981), 14-32. [4] S. S. Benchalli, R. S. Wali and Basavaraj M. Ittanagi on fuzzy rw-closed sets and fuzzy rw-open sets infuzzy topological spacesInt. J. of Mathematical Sciences and Applications, Vol. 1, No. 2, May 2011. [5] N. Nagaveni, Studies on Generalizations of Homeomorphisms in Topological Spaces, Ph.D.Thesis, Bharathiar University, Coimbatore, 1999. [6] Munkerjee, M.N.Sinha,,S.P.Irresolute and almost open functions between fts,fuzzy sets and systems , 29(1989)381-388. [7] R. S. Wali and Vivekananda Dembre;fuzzy sgw-continuous maps and fuzzy sgw-irresolute in fts. [8] A.Vadivel & K.vairamamanickam,rg?-Closed sets& rg?-open sets in Topological Spaces,Int J of math ,Analysis Vol 3, (2009)37,1803-1819. [9] Thakur S.S. and Bajpai Pandey Jyoti“Intuitionistic Fuzzy rg?-closed sets”, International Journal of Fuzzy system and Rough System 4(1), 67-73.

Copyright

Copyright © 2023 Dr. Vivekananda Dembre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.