Dow, Alan 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 Fundam. Math. 157, No. 1, 33-41 (1998). 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. Cited in 3 Documents MSC: 54A35 Consistency and independence results in general topology 03E35 Consistency and independence results 54G05 Extremally disconnected spaces, \(F\)-spaces, etc. PDFBibTeX XMLCite \textit{A. Dow}, Fundam. Math. 157, No. 1, 33--41 (1998; Zbl 0996.54008) Full Text: EuDML