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

Colloquium Mathematicae (1993)

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

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topJełowicki, 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

top- [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. Zbl0166.18602
- [3] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955. Zbl0068.01904
- [4] R. C. Walker, The Stone-Čech Compactification, Springer, Berlin, 1974. Zbl0292.54001
- [5] H. Wallman, Lattices and topological spaces, Ann. of Math. 39 (1938), 112-126. Zbl0018.33202

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