منابع مشابه
Rothberger's Property and Partition Relations
Let X be an infinite but separable metric space. An open cover U of X is said to be large if, for each x ∈ X the set {U ∈ U : x ∈ U} is infinite. The symbol Λ denotes the collection of large open covers of X. An open cover U of X is said to be an ω–cover if for each finite subset F of X there is a U ∈ U such that F ⊆ U , and X is not a member of U . X is said to have Rothberger’s property if th...
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The partition relation Ri-*0*i)ï,a, which was known to contradict the continuum hypothesis [1], is disproved without this hypothesis. For cardinals k^.co and X>1, let P{k, X) be the following partition relation: For any mapping F of the set [k]2 of unordered pairs of elements of k into X, there is a set B<=,k, of cardinality \B\ = k, such that the image of [B]2 under F is not all of X. Such a s...
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For each space, Ufin(Γ,Ω) is equivalent to Sfin(Ω,O) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindelöf space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Contin...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04513-x