TL;DR
This paper establishes a characterization of sober metric spaces within the framework of approach spaces, showing that such spaces are exactly those that are Smyth complete.
Contribution
It provides a precise equivalence between sobriety in approach spaces and Smyth completeness in metric spaces.
Findings
Sober approach spaces correspond to Smyth complete metric spaces
Characterization of sobriety in the context of approach spaces
Bridging metric completeness and topological sobriety
Abstract
It is proved that a metric space is sober, as an approach space, if and only if it is Smyth complete.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Fuzzy and Soft Set Theory · Homotopy and Cohomology in Algebraic Topology