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

Jan Jełowicki

Colloquium Mathematicae (1993)

  • Volume: 66, Issue: 2, page 209-217
  • ISSN: 0010-1354

Abstract

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The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto ( β ) 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 and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to the extension of the group operation. All the results involve the existence of R-points.

How to cite

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Jełowicki, Jan. "On extension of the group operation over the Čech-Stone compactification." Colloquium Mathematicae 66.2 (1993): 209-217. <http://eudml.org/doc/210243>.

@article{Jełowicki1993,
abstract = {The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto $(β)^2$ 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 and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to the extension of the group operation. All the results involve the existence of R-points.},
author = {Jełowicki, Jan},
journal = {Colloquium Mathematicae},
keywords = {convolution of ultrafilters; extension},
language = {eng},
number = {2},
pages = {209-217},
title = {On extension of the group operation over the Čech-Stone compactification},
url = {http://eudml.org/doc/210243},
volume = {66},
year = {1993},
}

TY - JOUR
AU - Jełowicki, Jan
TI - On extension of the group operation over the Čech-Stone compactification
JO - Colloquium Mathematicae
PY - 1993
VL - 66
IS - 2
SP - 209
EP - 217
AB - The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto $(β)^2$ 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 and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to the extension of the group operation. All the results involve the existence of R-points.
LA - eng
KW - convolution of ultrafilters; extension
UR - http://eudml.org/doc/210243
ER -

References

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  1. [1] E. K. van Douwen, Remote points, Dissertationes Math. 188 (1981). 
  2. [2] Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87-91. Zbl0166.18602
  3. [3] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955. Zbl0068.01904
  4. [4] R. C. Walker, The Stone-Čech Compactification, Springer, Berlin, 1974. Zbl0292.54001
  5. [5] H. Wallman, Lattices and topological spaces, Ann. of Math. 39 (1938), 112-126. Zbl0018.33202

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