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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 3, Pages 19–24 (Mi vuu333)  

This article is cited in 7 scientific papers (total in 7 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: ompactification, Stone space of Boolean algebra, chain, antichain.

Full text: PDF file (145 kB)
References: PDF file   HTML file
UDC: 515.122.536
MSC: 54D35
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

Citation in format AMSBIB
\Bibitem{Gol12}
\by R.~A.~Golovastov
\paper About Stone space of one Boolean algebra
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 3
\pages 19--24
\mathnet{http://mi.mathnet.ru/vuu333}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Gryzlov, R. A. Golovastov, “O prostranstvakh Stouna nekotorykh bulevykh algebr”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 1, 11–16  mathnet
    2. A. A. Gryzlov, R. A. Golovastov, “O plotnosti i chisle Suslina podmnozhestv odnogo prostranstva Stouna”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 4, 18–24  mathnet
    3. R. A. Golovastov, “Prostranstva Stouna nekotorykh bulevykh algebr”, Izv. IMI UdGU, 2015, no. 1(45), 3–36  mathnet  elib
    4. A. G. Chentsov, “Bitopological spaces of ultrafilters and maximal linked systems”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S24–S39  mathnet  crossref  crossref  mathscinet  isi  elib
    5. A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy: osnovnye sootnosheniya”, Izv. IMI UdGU, 53 (2019), 138–157  mathnet  crossref  elib
    6. A. G. Chentsov, “O superkompaktnosti prostranstva ultrafiltrov s topologiei volmenovskogo tipa”, Izv. IMI UdGU, 54 (2019), 74–101  mathnet  crossref
    7. A. G. Chentsov, “Superkompaktnye prostranstva ultrafiltrov i maksimalnykh stseplennykh sistem”, Tr. IMM UrO RAN, 25, no. 2, 2019, 240–257  mathnet  crossref  elib
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