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## Archive of Issues

Russia Izhevsk
Year
2012
Issue
3
Pages
19-24
 Section Mathematics Title About Stone space of one Boolean algebra Author(-s) Golovastov R.A.a Affiliations Udmurt State Universitya Abstract We consider the Boolean algebra of the same type as algebra constructed by Bell, and the Stone space of this Boolean algebra. This space is a compactification of a countable discrete space $N$. We prove that there are isolated points in a remainder of this compactification, which are limits of some convergent sequences. We prove that a clopen subset of our space, which is homeomorphic to $\beta\omega$, is a closure of the union of finitely many antichains from $N$. We construct two examples: a clopen subset of the remainder without isolated points, which is not homeomorphic to $\beta\omega\setminus\omega$; a subset of the remainder which is homeomorphic to $\beta\omega\setminus\omega$, but is not a clopen. Keywords сompactification, Stone space of Boolean algebra, сhain, antichain UDC 515.122.536 MSC 54D35 DOI 10.20537/vm120303 Received 30 May 2012 Language Russian Citation Golovastov R.A. About Stone space of one Boolean algebra, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 3, pp. 19-24. References Bell M.G. Compact ccc non-separable spaces of small weight, Topology Proceedings, 1980, vol. 5, pp. 11-25. Gryzlov A.A., Bastrykov E.S., Golovastov R.A. On Bell's compactification of $N$, Topology Proceedings, 2010, vol. 35, pp. 177-185. Bastrykov E.S. About some points of Bell's compactification of countable discrete space, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2009, no. 4, pp. 3-6. Gryzlov A.A., Bastrykov E.S., Golovastov R.A. About points of compactification of $N$, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2010, no. 3, pp. 10-17. Gryzlov A.A. On convergent sequences and copies of $\beta N$ in one compactification of $N$, XI Prague Symposium on General Topology, Prague, Czech Rep, 2011, p. 29. Golovastov R.A. About one compactifications of countable discrete space, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 1, pp. 14-19. Full text