On the cardinality and weight spectra of compact spaces, II

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\ < 2λ or \B\ = |B|λ; moreover, if X is the Stone space of B then either |X| ≤ 22λ or |X\ = |B| =\B|λ. This implies the existence of 0-dimensional compact T2 spaces whose cardinality and weight spectra omit lots of singular cardinals of "small" cofinality.