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Russia Izhevsk
Year
2014
Issue
4
Pages
18-24
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Section Mathematics
Title On the density and Suslin number of subsets of one Stone space
Author(-s) Gryzlov A.A.a, Golovastov R.A.a
Affiliations Udmurt State Universitya
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
UDC 515.122.536
MSC 54D35
DOI 10.20537/vm140402
Received 10 October 2014
Language Russian
Citation Gryzlov A.A., Golovastov R.A. On the density and Suslin number of subsets of one Stone space, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 4, pp. 18-24.
References
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