# On the cardinality and weight spectra of compact spaces, II

Fundamenta Mathematicae (1998)

- Volume: 155, Issue: 1, page 91-94
- ISSN: 0016-2736

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topJuhász, 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 -

## References

top- [vD] E. K. van Douwen, Cardinal functions on compact F-spaces and on weakly countably complete Boolean algebras, Fund. Math. 114 (1981), 235-256. Zbl0506.54006
- [J] I. Juhász, On the weight-spectrum of a compact space, Israel J. Math. 81 (1993), 369-379. Zbl0799.54002

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