Generalized metric spaces: Completion, topology, and powerdomains via the Yoneda embedding
نویسندگان
چکیده
منابع مشابه
Generalized Metric Spaces: Completion, Topology, and Powerdomains via the Yoneda Embedding
Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973). Combining Lawvere’s (1973) enriched-categorical and Smyth’s (1988, 1991) topological view on generalized metric spaces, it is shown how to construct (1) completion, (2) two topologies, and (3) powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ...
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Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces (Lawvere 1973, Rutten 1995). Combining Lawvere's (1973) enriched-categorical and Smyth' (1987, 1991) topological view on generalized (ultra)metric spaces, it is shown how to construct 1. completion, 2. topology, and 3. powerdomains for generalized ultrametric spaces. Restricted to the special...
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Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere 1973). Combining Lawvere's (1973) enriched-categorical and Smyth' (1988, 1991) topological view on generalized metric spaces, it is shown how to construct 1. completion , 2. topology, and 3. powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ordinary m...
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متن کاملLocalic Completion of Generalized Metric Spaces I
Following Lawvere, a generalized metric space (gms) is a set X equipped with a metric map from X to the interval of upper reals (approximated from above but not from below) from 0 to ∞ inclusive, and satisfying the zero self-distance law and the triangle inequality. We describe a completion of gms’s by Cauchy filters of formal balls. In terms of Lawvere’s approach using categories enriched over...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1998
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(97)00042-x