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Russia Izhevsk
Section  Mathematics 
Title  About Stone space of one Boolean algebra 
Author(s)  Golovastov R.A.^{a} 
Affiliations  Udmurt State University^{a} 
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  сompactification, Stone space of Boolean algebra, сhain, antichain 
UDC  515.122.536 
MSC  54D35 
DOI  10.20537/vm120303 
Received  30 May 2012 
Language  Russian 
Citation  Golovastov R.A. About Stone space of one Boolean algebra, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 3, pp. 1924. 
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