On the weight-spectrum of a compact space |
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Authors: | I Juhász |
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Institution: | (1) Department of Mathematics, Kansas State University, 66506 Manhattan, KS, USA;(2) Math. Inst. Hung. Acad. Sci., P.O. Box 127, 1364 Budapest, Hungary |
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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].
Research supported by OTKA grant no. 1908. |
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