On the cardinality and weight spectra of compact spaces, II

Juhász, Istvan; Shelah, Saharon

Fundamenta Mathematicae, Tome 158 (1998), p. 91-94 / Harvested from The Polish Digital Mathematics Library

Résumé

Let B(κ,λ) be the subalgebra of P(κ) generated by ${[κ]}^{\leq λ}$ . 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 $| X | \leq 2^{2^{λ}}$ 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.

Publié le : 1998-01-01

Zbl 0896.54001

EUDML-ID : urn:eudml:doc:212245

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     author = {Istvan Juh\'asz and Saharon Shelah},
     title = {On the cardinality and weight spectra of compact spaces, II},
     journal = {Fundamenta Mathematicae},
     volume = {158},
     year = {1998},
     pages = {91-94},
     zbl = {0896.54001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv155i1p91bwm}
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Juhász, Istvan; Shelah, Saharon. On the cardinality and weight spectra of compact spaces, II. Fundamenta Mathematicae, Tome 158 (1998) pp. 91-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv155i1p91bwm/

Bibliographie

[00000] [vD] E. K. van Douwen, Cardinal functions on compact F-spaces and on weakly countably complete Boolean algebras, Fund. Math. 114 (1981), 235-256. | Zbl 0506.54006

[00001] [J] I. Juhász, On the weight-spectrum of a compact space, Israel J. Math. 81 (1993), 369-379. | Zbl 0799.54002