The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces
نویسندگان
چکیده
منابع مشابه
The universal separable metric space of Urysohn and isometric embeddings thereof in Banach spaces
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 isometri...
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We introduce a model of the set of all Polish (=separable complete metric) spaces which is the cone R of distance matrices, and consider the geometrical and probabilistic problems connected with this object. We prove that the generic Polish space in the sense of this model is the so called universal Urysohn space which was defined by P.S.Urysohn in the 1920-th. Then we consider the metric space...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1992
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-140-3-199-223