Not all semiregular Urysohn-closed spaces are Katětov-Urysohn
نویسندگان
چکیده
منابع مشابه
Weakly Continuously Urysohn Spaces
We study weakly continuously Urysohn spaces, which were introduced in [Z]. We show that every weakly continuously Urysohn w∆-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monontonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountabl...
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A subset A of a metric space (X, d) is central iff for every Katětov map f : X → R upper bounded by the diameter of X and any finite subset B of X there is x ∈ X such that f(a) = d(x, a) for each a ∈ A ∪ B. Central subsets of the Urysohn universal space U (see introduction) are studied. It is proved that a metric space X is isometrically embeddable into U as a central set iff X has the collinea...
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In this informal note, we demonstrate the existence of forking and nondividing formulas in continuous theory of the complete Urysohn sphere, as well as the discrete theories of the integral Urysohn spaces of diameter n (where n ≥ 3). Whether or not such formulas existed was asked in thesis work of the author, as well as joint work with Terry. We also show an interesting phenomenon in that, for ...
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Let F (X) and A(X) be respectively the free topological group and the free Abelian topological group on a Tychonoff space X. For every natural number n we denote by Fn(X) (An(X)) the subset of F (X) (A(X)) consisting of all words of reduced length ≤ n. It is well known that if a space X is not discrete, then neither F (X) nor A(X) is Fréchet-Urysohn, and hence first countable. On the other hand...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1970-0257955-9