### I. Juhász, S. Shelah

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

Let `B(kappa,lambda)` be the subalgebra of
`P(\kappa)`
generated by `[kappa]^{<= lambda}``. It is shown that if
``B` is any
homomorphic image of `B(kappa,lambda)` then either
`|B|<2^lambda` or
`|B|=|B|^lambda`, moreover if `X` is the Stone space of
`B` then either
`|X|<= 2^{2^lambda}` or `|X|=|B|=|B|^\lambda`.

`
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This implies the existence of 0-dimensional compact `T_2` spaces whose
cardinality and weight spectra omit lots of singular cardinals of ``small''
cofinality.

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