Metric spaces in which Prohorov's theorem is not valid
Preiss, D.
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Preiss, D.
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McCandless, Byron H. (1963)
Portugaliae mathematica
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K. Alster (1982)
Colloquium Mathematicae
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Tibor Neubrunn, Jaroslav Smítal, Tibor Šalát (1967)
Časopis pro pěstování matematiky
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J. de Groot, R. McDowell (1960)
Fundamenta Mathematicae
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Julien Melleray (2010)
Fundamenta Mathematicae
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Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space ℓ²(ℕ). The proof is based on a lemma about extensions of metric spaces by finite metric spaces, which we also use to investigate (answering a question of I. Goldbring) the relationship, when A,B are finite subsets of the Urysohn space, between the group of isometries fixing A pointwise,...
Roman Duda, Rastislav Telgársky (1968)
Czechoslovak Mathematical Journal
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Szymon Plewik, Marta Walczyńska (2016)
Banach Center Publications
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By studying dimensional types of metric scattered spaces, we consider the wider class of metric σ-discrete spaces. Applying techniques relevant to this wider class, we present new proofs of some embeddable properties of countable metric spaces in such a way that they can be generalized onto uncountable metric scattered spaces. Related topics are also explored, which gives a few new results.
J. Melleray, F. V. Petrov, A. M. Vershik (2008)
Fundamenta Mathematicae
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We consider the problem of isometric embedding of metric spaces into Banach spaces, and introduce and study the remarkable class of so-called linearly rigid metric spaces: these are the spaces that admit a unique, up to isometry, linearly dense isometric embedding into a Banach space. The first nontrivial example of such a space was given by R. Holmes; he proved that the universal Urysohn space has this property. We give a criterion of linear rigidity of a metric space, which allows...
K. Van Doren (1973)
Fundamenta Mathematicae
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R. Pol (1975)
Colloquium Mathematicae
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