Point classes of compactifications of discrete spaces

E. S. Bastrykov

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 41 (2013) no. 1, pp. 47-77.

Résumé

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.

Détail

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

Bibliographie

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