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Izv. IMI UdGU, 2013, Issue 1(41), Pages 47–77 (Mi iimi248)  

Point classes of compactifications of discrete spaces

E. S. Bastrykov

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034

Abstract: We consider the compactification of one countable discrete space. This compactification is constructed as the Stone space of some Boolean algebra. We obtained some classes of points of remainder of this space, found dependence to the closures of countable subsets of these classes and also proved the existence of subsets of remainder whose closures are homeomorphic to a minimal (one-point) compactification of a countable discrete space, and subsets whose closure is homeomorphic to the Stone–Ĉzech space. We considered other properties of this space.

Keywords: compactification, Stone–Ĉzech space, discrete space, convergent sequence, Stone space of Boolean algebra.

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UDC: 515.122.536
MSC: 54D35, 54D80, 54-06
Received: 01.02.2013

Citation: E. S. Bastrykov, “Point classes of compactifications of discrete spaces”, Izv. IMI UdGU, 2013, no. 1(41), 47–77

Citation in format AMSBIB
\Bibitem{Bas13}
\by E.~S.~Bastrykov
\paper Point classes of compactifications of discrete spaces
\jour Izv. IMI UdGU
\yr 2013
\issue 1(41)
\pages 47--77
\mathnet{http://mi.mathnet.ru/iimi248}


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  • Известия Института математики и информатики Удмуртского государственного университета
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