منابع مشابه
Intersections of Shifted Sets
We consider shifts of a set A ⊆ N by elements from another set B ⊆ N, and prove intersection properties according to the relative asymptotic size of A and B. A consequence of our main theorem is the following: If A = {an} is such that an = o(n k/k−1), then the k-recurrence set Rk(A) = {x | |A∩ (A+ x)| > k} contains the distance sets of some arbitrarily large finite sets.
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We prove that the Covering Property Axiom CPAprism, which holds in the iterated perfect set model, implies the following facts. • If G is an intersection of ω1-many open sets of a Polish space and G has cardinality continuum, then G contains a perfect set. • There exists a subset G of the Cantor set which is an intersection of ω1-many open sets but is not a union of ω1-many closed sets. The exa...
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Various kinds of closed centred sets in normed spaces are considered. Necessary and sufficient conditions are obtained for every decreasing sequence of such sets to have nonempty intersection. Let X be a real or complex normed space. Recall that a set S ⊆ X is symmetric if S = −S and balanced if tS ⊆ S for all t ∈ [−1, 1]. It is convenient to introduce the following definitions. Definitions. 1....
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4861