A domain-theoretic approach to fuzzy metric spaces

We introduce a partial order ⊑M on the set BX of formal balls of a fuzzy metric space (X,M,∧) in the sense of Kramosil and Michalek, and discuss some of its properties. We also characterize when the poset (BX,⊑M) is a continuous domain by means of a new notion of fuzzy metric completeness introduced...

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Bibliographic Details
Published in:Topology and its applications 2014-02, Vol.163, p.149-159
Main Authors: Ricarte, Luis A., Romaguera, Salvador
Format: Article
Language:English
Subjects:
Continuous domain
Formal ball
Fuzzy metric space
Poset
Standard complete
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Summary:We introduce a partial order ⊑M on the set BX of formal balls of a fuzzy metric space (X,M,∧) in the sense of Kramosil and Michalek, and discuss some of its properties. We also characterize when the poset (BX,⊑M) is a continuous domain by means of a new notion of fuzzy metric completeness introduced here. The well-known theorem of Edalat and Heckmann that a metric space is complete if and only if its poset of formal balls is a continuous domain, is deduced from our characterization.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2013.10.014