Ditopological texture spaces and intuitionistic sets

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].…”

“…The following important theorem, which is proved in [3] gives a characterization of dicompactness in textures.…”

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

“…The analogous notion, and its dual, were given for ditopologies in [5], and studied in greater detail in [11]. We now wish to generalize these concepts for β-open and β-closed sets.…”

“…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.…”

“…The study of compactness in ditopological texture spaces was begun in [5], continued in [11,24] and extended to real compactness in [25]. In this paper we place β-compactness in a ditopological setting.…”