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Ultracompanions of subsets of a group

I. Protasov, S. Slobodianiuk (2014)

Commentationes Mathematicae Universitatis Carolinae

Let G be a group, β G be the Stone-Čech compactification of G endowed with the structure of a right topological semigroup and G * = β G G . Given any subset A of G and p G * , we define the p -companion Δ p ( A ) = A * G p of A , and characterize the subsets with finite and discrete ultracompanions.

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