Ditopological texture spaces and fuzzy topology, I. Basic concepts

Di-uniformities and Hutton uniformities

“…General references on ditopological texture spaces include [1,2,3,4,5,6] and constant reference will be made to [13,14,15,16,17] for definitions and results relating to di-uniformities. Our standart references for quasi uniformity are [7,8,9].…”

“…Direlations: [5] Let (S, S), (T, T) be textures. We use P (s,t) , Q (s,t) to denote the p-sets and q-sets for the product texture (S × T, P(S) ⊗ T).…”

β-open and β-closed sets in ditopological texture spaces

“…[6,8]), but we omit the details. In order to give useful characterizations of the above continuity properties we need the following definition.…”

“…Textures and ditopological texture spaces were first introduced by the second author as a point-based setting for the study fuzzy sets, and this line of investigation continues, see for example [5,6,8,9,10], and more recently [23]. On the other hand, textures offer a convenient setting for the investigation of complement-free concepts in general, so much of the recent work has proceeded independently of the fuzzy setting.…”

“…To complete this introduction we recall various concepts from [8,9] that will be needed later on in this paper.…”