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Section
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Mathematics
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Title
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About Stone space of one Boolean algebra
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Author(-s)
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Golovastov R.A.a
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Affiliations
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Udmurt State Universitya
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Abstract
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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.
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Keywords
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сompactification, Stone space of Boolean algebra, сhain, antichain
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UDC
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515.122.536
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MSC
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54D35
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DOI
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10.20537/vm120303
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Received
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30 May 2012
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Language
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Russian
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Citation
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Golovastov R.A. About Stone space of one Boolean algebra, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 3, pp. 19-24.
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References
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- 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.
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Full text
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