Geodesic
About Stone space of one Boolean algebra
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2012), pp. 19-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : сompactification, chain, antichain.
Keywords: Stone space of Boolean algebra 
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R. A. Golovastov. About Stone space of one Boolean algebra. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2012), pp. 19-24. http://geodesic.mathdoc.fr/item/VUU_2012_3_a2/

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