On the cardinality and weight spectra of compact spaces, II

Volume 155 / 1998

I. Juhász, S. Shelah Fundamenta Mathematicae 155 (1998), 91-94 DOI: 10.4064/fm-155-1-91-94


Let B(κ,λ) be the subalgebra of P(κ) generated by $[κ]^{≤λ}$. It is shown that if B is any homomorphic image of B(κ,λ) then either $|B| < 2^λ$ or $|B| = |B|^λ$; moreover, if X is the Stone space of B then either $|X| ≤ 2^{2^λ}$ or $|X| = |B| = |B|^λ$. This implies the existence of 0-dimensional compact $T_2$ spaces whose cardinality and weight spectra omit lots of singular cardinals of "small" cofinality.


  • I. Juhász
  • S. Shelah

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