Abstract
If a compact space K has a dense metrizable subspace its regular open algebra forces that the generic ultrafilter is countably generated. We investigate the class of compact spaces K for which the converse of this implication is true and give some applications of this. More precisely, we shall show that this gives us a rather powerful method for proving that a given compact space has a dense metrizable subspace especially in the case of compact subsets of sigma products of the unit interval.
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