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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, Issue 3, Pages 19–24
(Mi vuu333)
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This article is cited in 8 scientific papers (total in 8 papers)
MATHEMATICS
About Stone space of one Boolean algebra
R. A. Golovastov Department of Algebra and Topology, Udmurt State University, Izhevsk, Russia
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, chain, antichain.
Received: 30.05.2012
Citation:
R. A. Golovastov, “About Stone space of one Boolean algebra”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 3, 19–24
Linking options:
https://www.mathnet.ru/eng/vuu333 https://www.mathnet.ru/eng/vuu/y2012/i3/p19
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Abstract page: | 300 | Full-text PDF : | 173 | References: | 51 | First page: | 1 |
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