On two epireflective subcategories of the category of 2T0–fuzzy bitopological spaces

Abstract

The motivation for the present work is provided by Giuli and Salbany's work on the category BTOP₀ of T₀-bitopological spaces wherein they identified a cogenerator Q and a closure operator and used these to obtain, among other things, two interesting epireflective subcategories of BTOP₀ consisting of objects which they referred to as ‘absolutely 2T₀-closed' and ‘bisober' respectively. Moreover, the first such subcategory was also shown by them to be the epireflective hull of Q in BTOP₀. We show here that almost a perfectly analogous programme can be carried out within the category BFTS₀ of 2T₀-fuzzy bitopological spaces after identifying a key cogenerator in BFTS₀.

Keywords: 2T₀-fuzzy bitopological space, absolutely 2T₀-closed fuzzy bitopological space, sober fuzzy bitopological space, closure operator, epireflective subcategory, epireflective hull

Quaestiones Mathematicae 23(2000), 163–177