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A measure of thickness for families of sets

✍ Scribed by Antonín Le<anovsky; Vlastimil Pták

Publisher: Elsevier Science
Year: 1986
Tongue: English
Weight: 620 KB
Volume: 58
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(86)90184-6

No coin nor oath required. For personal study only.

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## A dual expression for the thickness of a family of sets is given. The thickness is a numerical characteristic of families of sets introduced in LeSanovsky and Ptak (1986). The dual expression is based on a simple combinatorial minimax result.

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We characterize the possible subsets of P(K) which can arise as the family of separated subsets of a closed discrete subset 6 of a topological (Hausdorff, regular or normal) space.

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✍ G. Freiman; E. Lipkin; L. Levitin 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 1003 KB

The present paper describes an algorithm for constructing families of k-independent subsets & of {1,2, . . . , n} with &I >2ck", where c, = d/(k -1)2& and d is a certain constant. The algorithm has a polynomial complexity with respect to the size of the family constructed.