Compactness in Smooth Bitopological Spaces

Abstract

The purpose of this paper is introducing the notion of smooth bitopological spaces. We define pairwise smooth-closure and pairwise smooth-interior of a fuzzy set and we study some of its properties. We give the definition for pairwise smooth compact set and show by an example that every pairwise smooth compact set need not be a smooth compact set. Finally we introduce the idea of pairwise smooth almost compact set and pairwise smooth nearly compact set.