On the cardinality and weight spectra of compact spaces, II

• Autorzy: Istvan Juhász , Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

cardinality and weight spectrum; compact space; homomorphism of Boolean algebras

Kategorie tematyczne

• 06E05: Structure theory
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 155
• Numer: 1
• Strony: 91-94

Daty

wydano

1997-04-10

Twórcy

autor

Istvan Juhász

• Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, Hungary,

autor

Saharon Shelah

• Institute of Mathematics, The Hebrew University, 91904 Jerusalem, Israel,
• Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.

Bibliografia

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