The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces
Fundamenta Mathematicae, Tome 140 (1991) no. 3, pp. 199-223
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This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0,1] of functions from [0,1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0,1]. It is shown that the closed linear span of an isometric copy of U in a Banach space which contains the zero of the Banach space is determined up to linear isometry. The question of what Banach spaces can be embedded in a linear isometric fashion in this uniquely determined closed linear span of U is investigated.
M. Randall Holmes. The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces. Fundamenta Mathematicae, Tome 140 (1991) no. 3, pp. 199-223. doi: 10.4064/fm-140-3-199-223
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author = {M. Randall Holmes},
title = {The universal separable metric space of {Urysohn} and isometric embeddings thereof in {{\CYRV}anach} spaces},
journal = {Fundamenta Mathematicae},
pages = {199--223},
year = {1991},
volume = {140},
number = {3},
doi = {10.4064/fm-140-3-199-223},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-140-3-199-223/}
}
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