Ultrafilters and almost disjoint sets

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Abstract

Let μκ denote the space of uniform ultrafilters on κ, and let λ be a cardinal. Uε{lunate}μκ is said to be a λ-point of μκ if U is a boundary point of λ pairwise disjoint open subsets of μκ. We prove that if κ is a successor cardinal, 2κ= κ+, and Kurepa's hypothesis for κ holds, then each U ε{lunate} μκ is a 2κ-point of μκ.

Original languageEnglish (US)
Pages (from-to)269-282
Number of pages14
JournalGeneral Topology and its Applications
Volume4
Issue number3
DOIs
StatePublished - Sep 1974

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