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Distributivity of the algebra of regular open subsets of .beta. R / R
- 1.0026231 - MÚ 2006 RIV NL eng J - Journal Article
Balcar, Bohuslav - Hrušák, M.
Distributivity of the algebra of regular open subsets of .beta. R / R.
[Distributivita algebry regulárních otevřených podmnožin .beta. R / R.]
Topology and its Applications. Roč. 149, č. 1 (2005), s. 1-7. ISSN 0166-8641. E-ISSN 1879-3207
R&D Projects: GA ČR(CZ) GA201/03/0933; GA ČR(CZ) GA201/02/0857
Institutional research plan: CEZ:AV0Z10190503
Keywords : distributivity of Boolean algebras * cardinal invariants of the continuum * Čech-Stone compactification
Subject RIV: BA - General Mathematics
Impact factor: 0.297, year: 2005
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.
Algebra regulárních otevřených podmnožin přírůstku Čech-Stoneovy kompaktifikace reálných čísel je píplnění algebry A.omega./fin, kde A značí algebru obojetných množin Cantorova diskontua. Je dokázáno, že distributivita této algebry je nejvýše rovna min.(h, add M), kde v add M značí additivita ideálu řídkých podmnožin reálných čísel.
Permanent Link: http://hdl.handle.net/11104/0116509
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