Geodesic
On the cardinality and weight spectra of compact spaces, II
Fundamenta Mathematicae, Tome 155 (1998) no. 1, pp. 91-94.

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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.
DOI : 10.4064/fm-155-1-91-94
Keywords: cardinality and weight spectrum, compact space, homomorphism of Boolean algebras

I. Juhász 1 ; S. Shelah 1

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I. Juhász; S. Shelah. On the cardinality and weight spectra of compact spaces, II. Fundamenta Mathematicae, Tome 155 (1998) no. 1, pp. 91-94. doi : 10.4064/fm-155-1-91-94. http://geodesic.mathdoc.fr/articles/10.4064/fm-155-1-91-94/

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