Distributivity of the algebra of regular open subsets of .beta. R / R
Distributivity of the algebra of regular open subsets of .beta. R / R
We compare the structure of the algebras P(.omega.)/fin and A.omega./Fin, where A denotes the algebra of clopen subsets of the Cantor set. We show that the distributivity number of the algebra A.omega./Fin is bounded by the distributivity number of the algebra P(.omega.)/fin and by the additivity of the meager ideal on the reals. As a corollary we obtain a result of A. Dow, who showed that in the iterated Mathias model the space .beta..omega./.omega. and .beta.R/R are not co-absolute. We also show that under the assumption t=h the spaces .beta..omega./.omega. and .beta.R/R are co-absolute, improving on a result of E. van Douwen.
- Academy of Sciences Library Czech Republic
Čech-Stone compactification, cardinal invariants of the continuum, distributivity of Boolean algebras
Čech-Stone compactification, cardinal invariants of the continuum, distributivity of Boolean algebras
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