TY - JOUR
T1 - On the cardinality and weight spectra of compact spaces, II
AU - Juhász, I.
AU - Shelah, S.
PY - 1998
Y1 - 1998
N2 - 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\ < 2λ or \B\ = |B|λ; moreover, if X is the Stone space of B then either |X| ≤ 22λ 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.
AB - 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\ < 2λ or \B\ = |B|λ; moreover, if X is the Stone space of B then either |X| ≤ 22λ 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.
KW - Cardinality and weight spectrum
KW - Compact space
KW - Homomorphism of Boolean algebras
UR - http://www.scopus.com/inward/record.url?scp=0012990837&partnerID=8YFLogxK
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AN - SCOPUS:0012990837
SN - 0016-2736
VL - 155
SP - 91
EP - 94
JO - Fundamenta Mathematicae
JF - Fundamenta Mathematicae
IS - 1
ER -