On isometrically universal spaces, mappings, and actions of groups (Q935254)
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scientific article; zbMATH DE number 5306964
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On isometrically universal spaces, mappings, and actions of groups |
scientific article; zbMATH DE number 5306964 |
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On isometrically universal spaces, mappings, and actions of groups (English)
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6 August 2008
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One could treat this paper as an addendum to the authors book [\textit{S. D. Illiadis}, Universal spaces and mappings, North-Holland Mathematics Studies 198. Amsterdam: Elsevier (2005; Zbl 1072.54001)], in particular to Sections 6.1 and 7.1 with the accent to isometries. In this direction notions are defined of isometrically universal mappings and isometrically universal \(G\)-spaces. Then the author explains how one modifies proofs in his book in order to see that the listed statements are correct. This is accompanied by 22 related problems. Here we bring a sample problem: Is there a metric on \(E^{2n+1}\) (Euclidean space) which makes it an isometrically containing space for the class of separable metrizable spaces of dimension \(\leq n\)?
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isometry
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Urysohn universal space
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universal mapping
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universal action of group
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