The Urysohn space embeds in Banach spaces in just one way

M. Randall Holmes

doi:10.1016/j.topol.2008.03.013

The Urysohn space embeds in Banach spaces in just one way

M. Randall Holmes

Mathematics Department

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In a Master's thesis in 1985 and a subsequent paper published in 1992, the author discovered that the universal separable metric space (up to isometry) discovered by Urysohn in 1925 has a uniquely determined linear closure (up to linear isometry) when isometrically embedded in a Banach space so as to include the zero of the Banach space. The proof of this result is given in this note and the current status of some related questions is discussed.

Original language	English
Pages (from-to)	1479-1482
Number of pages	4
Journal	Topology and its Applications
Volume	155
Issue number	14
DOIs	https://doi.org/10.1016/j.topol.2008.03.013
State	Published - 15 Aug 2008

Keywords

Banach space
Isometry
Universal separable metric space

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10.1016/j.topol.2008.03.013

Cite this

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abstract = "In a Master's thesis in 1985 and a subsequent paper published in 1992, the author discovered that the universal separable metric space (up to isometry) discovered by Urysohn in 1925 has a uniquely determined linear closure (up to linear isometry) when isometrically embedded in a Banach space so as to include the zero of the Banach space. The proof of this result is given in this note and the current status of some related questions is discussed.",

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N2 - In a Master's thesis in 1985 and a subsequent paper published in 1992, the author discovered that the universal separable metric space (up to isometry) discovered by Urysohn in 1925 has a uniquely determined linear closure (up to linear isometry) when isometrically embedded in a Banach space so as to include the zero of the Banach space. The proof of this result is given in this note and the current status of some related questions is discussed.

AB - In a Master's thesis in 1985 and a subsequent paper published in 1992, the author discovered that the universal separable metric space (up to isometry) discovered by Urysohn in 1925 has a uniquely determined linear closure (up to linear isometry) when isometrically embedded in a Banach space so as to include the zero of the Banach space. The proof of this result is given in this note and the current status of some related questions is discussed.

KW - Banach space

KW - Isometry

KW - Universal separable metric space

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M3 - Article

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JO - Topology and its Applications

JF - Topology and its Applications

IS - 14

ER -

The Urysohn space embeds in Banach spaces in just one way

Abstract

Keywords

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