On the cardinality and weight spectra of compact spaces, II

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

1997-03-15

arxiv.org/abs/math/9703220v1

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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. 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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