Abstract and concrete categories
Abstract and concrete categories
Ditopological texture spaces and intuitionistic sets
Fuzzy Sets and Systems - Special issue on topics of the mathematics of fuzzy objects
Fuzzy sets as texture spaces: I. Representation theorems
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Jordan surfaces in discrete antimatroid topologies
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Textural approach to generalized rough sets based on relations
Information Sciences: an International Journal
Textures and covering based rough sets
Information Sciences: an International Journal
Fundamenta Informaticae - Advances in Rough Set Theory
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This paper is the first of a series of three papers on the theory of interior and closure operators. Here, the theory is discussed from the textural point of view. First, the interior and closure operators on texture spaces are defined and some basic properties are given in terms of neighbourhoods and coneigbourhoods. Then the category dfIC whose objects are interior-closure spaces and the morphisms are bicontinuous difunctions is shown to be topological over the ground category dfTex of textures and difunctions. Further, considering the closure operator on Hutton algebras (known as fuzzy lattices) in the sense of C@?ech, the category HutCl of Hutton closure spaces and continuous mappings is defined. Finally, the category cdfIC of complemented bicontinuous difunctions and complemented interior-closure texture spaces and the opposite category of HutCl are shown to be equivalent.