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Continuity and Algebraic Structure of the Urysohn space

2012/01/10 by Davorin Lešnik, Lešnik, Davorin
Computer Science · Mathematics · #54E99 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #math.MG #msc:54E99

paper · pdf · doi:10.48550/arxiv.1201.2077

arxiv created 2012/01/10 · openalex publication_date 2012/01/10 · arxiv updated 2012/01/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Urysohn space is a complete separable metric space, universal among separable metric spaces for extending finite partial isometries into it. We present an alternative construction of the Urysohn space which enables us to show that extending isometries can be done in a canonical and continuous way, and allows us to equip the Urysohn space with algebraic structure. This is achieved in a constructive setting without assuming any choice principles.

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