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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, Issue 4, Pages 18–24 (Mi vuu448)  

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

On the density and Suslin number of subsets of one Stone space

A. A. Gryzlova, R. A. Golovastov

a Department of Algebra and Topology, Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: The paper concerns the Stone space of the Boolean algebra of subsets of one countable partially ordered set. The main feature of this set is the existence of countably many successors of each of its elements. From this property it follows that every fixed ultrafilter of this Stone space is a nonisolated point; the subset of free ultrafilters is dense everywhere. The classification of space points is given; the fact that there are free ultrafilters, which are not limits of sequences of fixed ultrafilters, as well as free ultrafilters determined by chains of partially ordered set, is proved. The cardinal invariants of the subspace of free ultrafilters are considered. It is shown that this subspace has the countable Suslin number, but is not separable.

Keywords: Boolean algebra, Stone space of Boolean algebra, ultrafilter.

Full text: PDF file (195 kB)
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UDC: 515.122.536
MSC: 54D35
Received: 10.10.2014

Citation: A. A. Gryzlov, R. A. Golovastov, “On the density and Suslin number of subsets of one Stone space”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4, 18–24

Citation in format AMSBIB
\Bibitem{GryGol14}
\by A.~A.~Gryzlov, R.~A.~Golovastov
\paper On the density and Suslin number of subsets of one Stone space
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2014
\issue 4
\pages 18--24
\mathnet{http://mi.mathnet.ru/vuu448}


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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. R. A. Golovastov, “Prostranstva Stouna nekotorykh bulevykh algebr”, Izv. IMI UdGU, 2015, no. 1(45), 3–36  mathnet  elib
    2. A. G. Chentsov, “Superrasshirenie kak bitopologicheskoe prostranstvo”, Izv. IMI UdGU, 49 (2017), 55–79  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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