A Wallman-type compactification of texture spaces

Textural approach to generalized rough sets based on relations

“…respectively (for topological arguments on textures see [1,[4][5][6][7][8]10,11,17]). Product of textures can be defined in a natural way [3].…”

“…Hence, many properties of Hutton algebras (fuzzy lattices) can be discussed in terms of textures [3]. Ditopologies (dichotomous topologies) on textures unify the fuzzy topologies, topologies and bitopologies in a non-complemented setting by means of duality in the textural concepts [1,[4][5][6][7][8]10,11,17]. Direlations are defined between textures as the pairs of elements of the product of textures, that is if ðU; UÞ and ðT; TÞ are textures, then ðr; RÞ is a direlation from U to T where r; R 2 PðUÞ T [4].…”

Textures and -spaces

“…complete, completely distributive lattices equipped with order-reversing involutions [30]), L-fuzzy sets, generalized fuzzy sets and intuitionistic sets can be represented by some suitable textures [4,7,[9][10][11][12]. Although various (mainly topological) aspects of textures have been investigated by him and his colleagues [2,[7][8][9][10][11][12][13][14][15]26,27] comprehensively, there are still some fundamental questions which will be main subjects of this paper:…”