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On the cardinality and weight spectra of compact spaces, II

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Juhász I., Shelah S.

Fundamenta Mathematicae

1998

tom 155

nr 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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Juhász I.

1 Shelah S.

1 1998

Wyniki wyszukiwania

On the cardinality and weight spectra of compact spaces, II