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On extension of the group operation over the Čech-Stone compactification

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Jełowicki J.

Colloquium Mathematicum

1993

tom 66

nr 2

209-217

The convolution of ultrafilters of closed subsets of a normal topological group 𝕋 is considered as a substitute of the extension onto $(β𝕋)^2$ of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group 𝕃 and its dense subgroup 𝔾, we construct subsets of β𝔾 algebraically isomorphic to 𝕃. Finally, we check whether the natural mapping from β𝔾 onto β𝕃 is a homomorphism with respect to the extension of the group operation. All the results involve the existence of R-points.

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1 Colloquium Mathematicum

1 Jełowicki J.

1 1993

Wyniki wyszukiwania

On extension of the group operation over the Čech-Stone compactification