Revisiting di-uniformity and full-dinormality via dicovers

Abstract

In this paper, we dene and study the notions of normal* and w-anchored dicovers as important classes of covers, convenient for the texture theory. Especially, a ditopological counterpart is given for the well-known result that in a completely regular topological space, the collection of all normal covers forms a uniformity com-patible with the topology. In addition, we describe two kinds of dicovers called divisible and even, in order to characterize the largest di-uniformity on textures, as well as characterizing the full dinormality which is introduced by L.M. Brown and M. Diker (Paracompactness and full normality in ditopological texture spaces, J. Math. Annal. Appl. 227 (1998), 144{165).

Mathematics Subject Classication (2010): 06B23, 18B35, 54D20, 54E55.