The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces
Holmes, M.
Fundamenta Mathematicae, Tome 141 (1992), p. 199-223 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:211941 
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     title = {The universal separable metric space of Urysohn and isometric embeddings thereof in Vanach spaces},
     journal = {Fundamenta Mathematicae},
     volume = {141},
     year = {1992},
     pages = {199-223},
     zbl = {0772.54022},
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Holmes, M. The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces. Fundamenta Mathematicae, Tome 141 (1992) pp. 199-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv140i3p199bwm/

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