Pairwise fuzzy D-baire spaces

Thangaraj G,Sethuraman S

doi:10.26524/cm80

Abstract

In this paper we introduce the concept of D-Baire bitopological spaces and several properties are investigated.

Highlights

The theory of fuzzy sets was initiated by by L.A.Zadeh in his classical paper [12] in the year 1965 as an attempt to develop a mathematically precise framework in which to treat systems or phenomena which cannot themselves be characterized precisely
We introduce the concept of D-Baire bitopological spaces in fuzzy setting and investigate several characterizations of pairwise fuzzy D-Baire spaces
[8] If λ is a pairwise fuzzy nowhere dense set in a fuzzy bitopological space (X, T1, T2), 1 − λ is a pairwise fuzzy dense set in (X, T1, T2)

Summary

Introduction

The theory of fuzzy sets was initiated by by L.A.Zadeh in his classical paper [12] in the year 1965 as an attempt to develop a mathematically precise framework in which to treat systems or phenomena which cannot themselves be characterized precisely. The paper of C.L.Chang [3] in 1968 paved the way for the subsequent tremendous growth of the numerous fuzzy topological concepts. In 1989, A.Kandil [4] introduced the concept of fuzzy bitopological space as an extension and generalization of fuzzy topological space. Rene Baire introduced the concept of first and second category in topology. To define first category Baire, relied on Cantor’s definition of dense sets and P.du Bois-Reymond’s definition of nowhere dense sets.Denjoy introduced the concept residual as the sets which are complements of first category sets around 1912. The concept of Baire spaces in fuzzy setting was introduced and studied by G.Thangaraj and S.Anjalmose in [7]. The concept of Baire spaces in fuzzy bitopological setting was introduced and studied by the authors in [9]. We introduce the concept of D-Baire bitopological spaces in fuzzy setting and investigate several characterizations of pairwise fuzzy D-Baire spaces

Preliminaries

Pairwise fuzzy D-Baire spaces