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Russia Izhevsk
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 University^{a} 
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. 1824. 
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