Vol. 70, No. 1, 1977

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ISSN: 0030-8730
Attaining the spread at cardinals of cofinality ω

Kenneth Kunen and Judith Roitman

Vol. 70 (1977), No. 1, 199–205
Abstract

Let λ be a singular cardinal of cofinality ω. We investigate the question: does every Hausdorff space with spread λ have a discrete subspace of cardinality λ? The answer is “yes” if λ > 20 or if λ < 20 and MA holds; however, for λ < 20 an answer of “no” is consistent with the axioms of set theory. The proof involves showing the equivalence of the question with one about category in the real line. Similar results hold for the width of a space.

Mathematical Subject Classification
Primary: 02K30, 02K30
Milestones
Received: 14 January 1976
Published: 1 May 1977
Authors
Kenneth Kunen
Judith Roitman