The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto 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.
@article{bwmeta1.element.bwnjournal-article-cmv66i2p209bwm,
author = {Jan Je\l owicki},
title = {On extension of the group operation over the \v Cech-Stone compactification},
journal = {Colloquium Mathematicae},
volume = {66},
year = {1993},
pages = {209-217},
zbl = {0851.54027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv66i2p209bwm}
}
Jełowicki, Jan. On extension of the group operation over the Čech-Stone compactification. Colloquium Mathematicae, Tome 66 (1993) pp. 209-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv66i2p209bwm/
[000] [1] E. K. van Douwen, Remote points, Dissertationes Math. 188 (1981).
[001] [2] Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87-91. | Zbl 0166.18602
[002] [3] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955. | Zbl 0068.01904
[003] [4] R. C. Walker, The Stone-Čech Compactification, Springer, Berlin, 1974. | Zbl 0292.54001
[004] [5] H. Wallman, Lattices and topological spaces, Ann. of Math. 39 (1938), 112-126. | Zbl 0018.33202