Constructive Urysohn's Universal Metric Space | Zendy

Davorin Lešnik | Zendy

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Constructive Urysohn's Universal Metric Space

Author(s) -

Davorin Lešnik

Publication year - 2008

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2008.12.015

Subject(s) - mathematics , metric space , injective metric space , isometry (riemannian geometry) , convex metric space , linear subspace , constructive , uniform continuity , pure mathematics , context (archaeology) , urysohn and completely hausdorff spaces , isomorphism (crystallography) , space (punctuation) , metric differential , metric (unit) , discrete mathematics , intrinsic metric , computer science , hausdorff dimension , paleontology , crystal structure , chemistry , operations management , process (computing) , hausdorff measure , economics , biology , crystallography , operating system

A construction of the Urysohn's universal metric space is given in the context of constructive theory of metric spaces. The space is universal in the sense that every separable metric space isometrically embeds into it. Moreover, every isometry between two finite subspaces extends to total isometry, and this determines the Urysohn space uniquely up to isometric isomorphism

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