On the cardinality and weight spectra of compact spaces, II

Juhász, Istvan, and Shelah, Saharon. "On the cardinality and weight spectra of compact spaces, II." Fundamenta Mathematicae 155.1 (1998): 91-94. <http://eudml.org/doc/212245>.

@article{Juhász1998,
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 $|X| ≤ 2^\{2^λ\}$ 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.},
author = {Juhász, Istvan, Shelah, Saharon},
journal = {Fundamenta Mathematicae},
keywords = {cardinality and weight spectrum; compact space; homomorphism of Boolean algebras},
language = {eng},
number = {1},
pages = {91-94},
title = {On the cardinality and weight spectra of compact spaces, II},
url = {http://eudml.org/doc/212245},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Juhász, Istvan
AU - Shelah, Saharon
TI - On the cardinality and weight spectra of compact spaces, II
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 1
SP - 91
EP - 94
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 $|B| < 2^λ$ 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.
LA - eng
KW - cardinality and weight spectrum; compact space; homomorphism of Boolean algebras
UR - http://eudml.org/doc/212245
ER -