On the cardinality and weight spectra of compact spaces, II

ArticleOriginal scientific text

Title

Authors ¹, ^2,³

Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, Hungary
Institute of Mathematics, The Hebrew University, 91904 Jerusalem, Israel
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.

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.

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

[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.