On the cardinality and weight spectra of compact spaces, II

I. Juhász; S. Shelah

doi:10.4064/fm-155-1-91-94

On the cardinality and weight spectra of compact spaces, II

I. Juhász^*
, S. Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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| ≤ 2^2λ or |X\ = |B| =\B|^λ. This implies the existence of 0-dimensional compact T₂ spaces whose cardinality and weight spectra omit lots of singular cardinals of "small" cofinality.

Original language	English
Pages (from-to)	91-94
Number of pages	4
Journal	Fundamenta Mathematicae
Volume	155
Issue number	1
DOIs	https://doi.org/10.4064/fm-155-1-91-94
State	Published - 1998

Keywords

Cardinality and weight spectrum
Compact space
Homomorphism of Boolean algebras

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KW - Homomorphism of Boolean algebras

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On the cardinality and weight spectra of compact spaces, II

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Keywords

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