A theorem on almost disjoint sets
نویسندگان
چکیده
منابع مشابه
Almost disjoint families on large underlying sets
We show that, for any poset P, the existence of a P-indestructible mad family F ⊆ [ω]א0 is equivalent to the existence of such a family over אn for some/all n ∈ ω. Under the very weak square principle ¤∗∗∗ ω1,μ of Fuchino and Soukup [7] and cf([μ]א0 ,⊆) = μ+ for all limit cardinals μ of cofinality ω, the equivalence for any proper poset P transfers to all cardinals. That is, under these assumpt...
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The cardinal power of a set A is denoted by IA . Two sets A,, A2 are said to e almost disjoint if IA1 U A2I < lA i l (i = 1, 2) . e call B a transversal of the disjoint non-empty sets A,, (v E M) if Bc U A,, and B intersects each A,. (v E M) in a singleton . D1 An old and well known theorem of W . SIERPINSKI is that an infinite set of po-ver m contains more than m subsets of power m which are p...
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We investigate the question which (separable metrizable) spaces have a ‘large’ almost disjoint family of connected (and locally connected) sets. Every compact space of dimension at least 2 as well as all compact spaces containing an ‘uncountable star’ have such a family. Our results show that the situation for 1-dimensional compacta is unclear. 2004 Elsevier B.V. All rights reserved.
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A combinatorial principle CECA is formulated and its equivalence with GCH + certain weakenings of 2λ for singular λ is proved. CECA is used to show that certain “almost point-< τ” families can be refined to point-< τ families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of “every first countable T1-space with a weakly uniform base ...
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must hold, where A(x) denotes the number of elements of A up to x. It is quite natural to ask how much the situation changes if we cut A into two parts, A' and A ", and demand only that no a i' a, should coincide with any a i ' -a,' . This question was proposed by Erdős and Graham in [2], and it seemed likely that no considerable increase can be achieved in the density of A . We shall show, how...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1971
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-24-1-1-2