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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, Issue 4, Pages 18–24
(Mi vuu448)
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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.
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
Linking options:
https://www.mathnet.ru/eng/vuu448 https://www.mathnet.ru/eng/vuu/y2014/i4/p18
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Abstract page: | 326 | Full-text PDF : | 144 | References: | 42 |
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