Universal metric spaces and extension dimension
نویسندگان
چکیده
منابع مشابه
1 6 A ug 1 99 9 UNIVERSAL METRIC SPACES AND EXTENSION DIMENSION
For any countable CW -complex K and a cardinal number τ ≥ ω we construct a completely metrizable space X(K, τ) of weight τ with the following properties: e-dimX(K, τ) ≤ K, X(K, τ) is an absolute extensor for all normal spaces Y with e-dimY ≤ K, and for any completely metrizable space Z of weight ≤ τ and e-dimZ ≤ K the set of closed embeddings Z → X(K, τ) is dense in the space C(Z,X(K, τ)) of al...
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We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone R of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance matrix is defined and we proved that the set of such matrices is everywhere dense Gδ set in weak topology in the cone R. Universality of distance matrix is the necess...
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Some generalizations of the classical Hurewicz formula are obtained for extension dimension and C-spaces. A characterization of the class of metrizable spaces which are absolute neighborhood extensors for all metrizable C-spaces is also given.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2001
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(00)00019-5