Categories of dicompact BI-T2 texture spaces and a Banach-stone theorem

Abstract

The principal aim of this paper is to consider various aspects of the theory of dicompact bi-T₂ texture spaces, and place them in a categorical setting. It culminates in a version of the Banach-Stone theorem. On the way, a new class of textures, called here nearly plain textures, is seen to play a crucial role in the development of the theory.

Keywords:texture; C-space; ditopology; dicompact; T-lattice; real texture; nearly-plain texture; category; equivalence; adjoint functor; Banach-Stone theorem

Quaestiones Mathematicae 30(2007), 167–192