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On the weight-spectrum of a compact space

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Abstract

The weight-spectrumSp(w, X) of a spaceX is the set of weights of all infinite closed subspaces ofX. We prove that ifκ>ω is regular andX is compactT 2 withω(X)≥κ then some λ withκ≤λ≤2<κ is inSp(ω, X). Under CH this implies that the weight spectrum of a compact space can not omitω 1, and thus solves problem 22 of [M]. Also, it is consistent with 2ω=c being anything it can be that every countable closed setT of cardinals less thanc withω ∈ T satisfiesSp(w, X)=T for some separable compact LOTSX. This shows the independence from ZFC of a conjecture made in [AT].

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Authors and Affiliations

  1. Department of Mathematics, Kansas State University, 66506, Manhattan, KS, USA

    I. Juhász

  2. Math. Inst. Hung. Acad. Sci., P.O. Box 127, 1364, Budapest, Hungary

    I. Juhász

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  1. I. Juhász
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Research supported by OTKA grant no. 1908.

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Juhász, I. On the weight-spectrum of a compact space. Israel J. Math. 81, 369–379 (1993). https://doi.org/10.1007/BF02764839

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  • DOI: https://doi.org/10.1007/BF02764839

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