On fuzzy monotone convergence Q-cotopological spaces
| Autor: | Qingguo Li, Kai Wang, Zhongxi Zhang, Fu-Gui Shi |
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| Rok vydání: | 2021 |
| Předmět: |
Subcategory
0209 industrial biotechnology Closed set Logic Quantale 02 engineering and technology Characterization (mathematics) Space (mathematics) Fuzzy logic Combinatorics 020901 industrial engineering & automation Monotone polygon Artificial Intelligence 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Commutative property Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 425:18-33 |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2020.11.021 |
| Popis: | 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 S Q -CTop of stratified Q -cotopological spaces onto the full subcategory S Q -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. |
| Databáze: | OpenAIRE |
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