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Set mappings defined on pairs
Published online by Cambridge University Press: 09 April 2009
Abstract
A set mapping on pairs over the set S is a function f such that for each unordered pair a of elements of S,f(a) is a subset of S disjoint from a. A subset H of S is said to be free for f if x∉ f({y, z}) for all x, y, z from H. In this paper, we investigate conditions imposed on the range of f which ensure that there is a large set free for f. For example, we show that if f is defined on a set of size K+ + with always |f(a)| <k then f has a free set of size K+ if the range of f satisfies the k-chain condition, or if any two sets in the range of f have an intersection of size less than θ for some θ with θ < K.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 356 - 365
- Copyright
- Copyright © Australian Mathematical Society 1981
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