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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...
In this work, we discuss interior and closure operators on textures in the sense of Dikranjan–Giuli. First, we define the category dfICL of interior–closure spaces and bicontinuous difunctions and show that it is topological over dfTex whose objects are textures and morphisms are difunctions. The category L-CLOSURE of L-closure spaces and Zadeh type powerset operators, and the counterparts of the...
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