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- W4387339509 abstract "In this paper, we consider a full subcategory S of the category CLQ of stratified Q-closure spaces, satisfying some conditions. We construct a reflection from the category CLQ onto S, called the S-completion, which encompasses a variety of completions for Q-closure spaces, Q-cotopological spaces, and Q-ordered sets. The notion of a fuzzy subset system Z on a category C of structured sets is introduced. By considering fuzzy subset systems Z on the category CLQ, we introduce the concept of a Z-convergence Q-closure space, as a generalization of sober/bounded sober/monotone convergence Q-cotopological spaces. We show that the category S is exactly a category of Z-convergence spaces for some fuzzy subset system Z. And, in the case that Z consists of irreducible fuzzy sets, the S-completion can be restricted to the setting of Q-cotopological spaces. The sobrification, bounded sobrification, D-completion of Q-cotopological spaces are special cases of the S-completion. After establishing the connections between fuzzy subset systems on CLQ and those on the category ORDQ of Q-ordered sets, we provide a general approach to generating various completions of Q-ordered sets from the S-completion of corresponding Q-closure spaces. Completions of Q-ordered sets with respect to different types of fuzzy directedness can be obtained directly in this useful framework." @default.
- W4387339509 created "2023-10-05" @default.
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- W4387339509 date "2023-12-01" @default.
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- W4387339509 title "A general categorical reflection for various completions of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:mi mathvariant=script>Q</mml:mi></mml:math>-closure spaces and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:mi mathvariant=script>Q</mml:mi></mml:math>-ordered sets" @default.
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- W4387339509 doi "https://doi.org/10.1016/j.fss.2023.108736" @default.
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