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- W3109519275 abstract "In this paper, we generalize the concept of a monotone convergence space (also called a d-space) to the setting of a Q-cotopological space, where Q is a commutative and integral quantale. We establish a D-completion for every stratified Q-cotopological space, which is a category reflection of the category SQ-CTop of stratified Q-cotopological spaces onto the full subcategory SQ-DCTop of monotone convergence Q-cotopological spaces. By introducing the notion of a tapered set, a direct characterization of the completion is obtained: the D-completion of each stratified Q-cotopological space X consists exactly of those tapered closed sets in X. We show that the D-completion can be applied to obtain a universal fuzzy directed completion of a Q-ordered set by endowing it with the Scott cotopology, taking the D-completion, and then passing to the specialization Q-order. Consequently, the category Q-DOrd of fuzzy directed complete Q-ordered sets and Scott continuous functions is reflective in the category Q-Ordσ of Q-ordered sets and Scott continuous functions." @default.
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- W3109519275 date "2021-11-01" @default.
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- W3109519275 title "On fuzzy monotone convergence <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:mi mathvariant=script>Q</mml:mi></mml:math>-cotopological spaces" @default.
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- W3109519275 doi "https://doi.org/10.1016/j.fss.2020.11.021" @default.
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