Israel Journal of Mathematics

, Volume 81, Issue 3, pp 369–379 | Cite as

On the weight-spectrum of a compact space

  • I. Juhász


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 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].


Compact Space Closed Subspace Inaccessible Cardinal Cardinal Function Singular Cardinal 
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Copyright information

© The Magnes Press 1993

Authors and Affiliations

  • I. Juhász
    • 1
    • 2
  1. 1.Department of MathematicsKansas State UniversityManhattanUSA
  2. 2.Math. Inst. Hung. Acad. Sci.BudapestHungary

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