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Two step iteration of almost disjoint families

Published online by Cambridge University Press:  12 March 2014

Jerry E. Vaughan
Jerry E. Vaughan*
Affiliation:
Department of Mathematical Sciences, University of North Carolina, at Greensboro, Greensboro, NC 27402, USA, E-mail: vaughanj@uncg.edu
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Extract

Let E be an infinite set, and [E]ω the set of all countably infinite subsets of E. A family ⊂ [E]ω is said to be almost disjoint (respectively, pairwise disjoint) provided for A, B ∈ , if A ≠ B then A ∩ B is finite (respectively, A ∩ B is empty). Moreover, an infinite family A is said to be a maximal almost disjoint family provided it is an infinite almost disjoint family not properly contained in any almost disjoint family. In this paper we are concerned with the following set of topological spaces defined from (maximal) almost disjoint families of infinite subsets of the natural numbers ω.

Keywords

almost disjoint familiessmall uncountable cardinalsiterations of ψHausdorffUrysohn
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 1 , March 2004 , pp. 81 - 90
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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