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- W2916823488 abstract "We provide some new characterizations of L-convex spaces by using the way-below relation in domain theory. For this purpose, we first study the notion of domain finiteness in the lattice-valued case, and then introduce three kinds of spaces: algebraic L-closure spaces, restricted L-hull spaces, and L-entailment spaces. These three spaces are shown to be categorically isomorphic to L-convex spaces. Additionally, we introduce the notion of L-polytopes and prove that a subcollection of a dense L-convex structure is a base if and only if it contains all L-polytopes. These results indicate that in the study of the theory of (fuzzy) convex spaces, (fuzzy) domain theory has important applications." @default.
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- W2916823488 date "2020-02-01" @default.
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- W2916823488 title "Characterizations of L-convex spaces via domain theory" @default.
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- W2916823488 doi "https://doi.org/10.1016/j.fss.2019.02.009" @default.
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