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

• Autorzy: Jan Jełowicki
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 66
• Numer: 2
• Strony: 209-217

Daty

wydano

1993

otrzymano

1992-01-20

poprawiono

1992-11-28

Twórcy

autor

Jan Jełowicki

• Department of Mathematics, Agricultural Academy of Wrocław, Norwida 25, 50-375 Wrocław, Poland

Bibliografia

• [1] E. K. van Douwen, Remote points, Dissertationes Math. 188 (1981).
• [2] Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87-91.
• [3] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955.
• [4] R. C. Walker, The Stone-Čech Compactification, Springer, Berlin, 1974.
• [5] H. Wallman, Lattices and topological spaces, Ann. of Math. 39 (1938), 112-126.