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Section
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Mathematics
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Title
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The Stone spaces of Boolean algebras
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Author(-s)
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Gryzlov A.A.a,
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 Stone spaces $BD$ and $BS$ of two Boolean algebras. We prove, that the subspace of free ultrafilters of the space $BD$, and the space $BS$ are homeomorphic to the Cantor set.
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Keywords
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Boolean algebra, Stone space of Boolean algebra, ultrafilter, сompact
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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/vm130102
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Received
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11 February 2013
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Language
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Russian
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Citation
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Gryzlov A.A., Golovastov R.A. The Stone spaces of Boolean algebras, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 1, pp. 11-16.
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References
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- Alexandrov P.S. Vvedenie v teoriyu mnozhestv i obshchuyu topologiyu (Introduction to set theory and general topology), Moscow: Nauka, 1977, 368 p.
- Gryzlov A.A., Bastrykov E.S., Golovastov R.A. On Bell’s compactification of N, Topology Proceedings, 2010, vol. 35, pp. 177–185.
- 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.
- Golovastov R.A. About one compactifications of countable discrete space, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 1, pp. 14–19.
- Golovastov R.A. About Stone space of one Boolean algebra, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2012, no. 3, pp. 19–24.
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Full text
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