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The regular open algebra of \(\beta\mathbb{R}\backslash \mathbb{R}\) is not equal to the completion of \({\mathcal P}(\omega)/\text{fin}\). (English) Zbl 0996.54008

Summary: Two compact spaces are co-absolute if their respective regular open algebras are isomorphic (i.e. homeomorphic Gleason covers). We prove that it is consistent that \(\beta\omega \smallsetminus\omega\) and \(\beta \mathbb{R} \smallsetminus\mathbb{R}\) are not co-absolute.

MSC:

54A35 Consistency and independence results in general topology
03E35 Consistency and independence results
54G05 Extremally disconnected spaces, \(F\)-spaces, etc.
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