Connections between realcompactifications in various categories

Abstract

The author gives a detailed analysis of the relation between the theories of realcompactications and compactications in the category of ditopological texture spaces and in the categories of bitopological spaces and topological spaces.

Keywords: Bitopology, texture, ditopology, Stone-Čech compactication, Hewitt real- compactication, refector, T-lattice, real dicompactness, equivalence, adjoint functor, natural transformation.