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Scott approach distance on metric spaces

2016/10/20 by Wei Li, Li, Wei, Dexue Zhang +1
Decision Sciences · Mathematics · #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1610.06341

openalex publication_date 2016/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notion of Scott distance between points and subsets in a metric space, a metric analogy of the Scott topology on an ordered set, is introduced, making a metric space into an approach space. Basic properties of Scott distance are investigated, including its topological coreflection and its relation to injective T0 approach spaces. It is proved that the topological coreflection of the Scott distance is sandwiched between the d-Scott topology and the generalized Scott topology; and that every injective T0 approach space is a cocomplete and continuous metric space equipped with its Scott distance.

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