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Actions of Semitopological Groups

Published online by Cambridge University Press:  04 January 2019

Jan van Mill
Affiliation:
Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, P. O. Box 94248, 1090 GE Amsterdam, Netherlands Email: [email protected]
Vesko M. Valov
Affiliation:
Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay ON P1B 8L7 Email: [email protected]
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Abstract

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We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.

Type
Article
Copyright
© Canadian Mathematical Society 2018 

Footnotes

Author J. v. M. is pleased to thank the Department of Mathematics at Nipissing University for generous hospitality and support. Author V. M. V. was partially supported by NSERC Grant 261914-13.

References

Arens, R., Topologies for homeomorphism groups . Amer. J. Math. 68(1946), 593610. https://doi.org/10.2307/2371787.Google Scholar
Arhangel’skii, A. and Reznichenko, E., Paratopologivcal and semitopological groups versus topological groups . Topology Appl. 151(2005), 107119. https://doi.org/10.1016/j.topol.2003.08.035.Google Scholar
Arhangel’skii, A. and Tkachenko, M., Topological groups and related structures . Atlantis Studies in Mathematics, 1. Atlantis Press, Paris; World Scientific, Hackensack, NJ, 2008.Google Scholar
Chatyrko, V. and Kozlov, K., Topological transformation groups and Dugundji compact Hausdorff spaces . (Russian) Mat. Sb. 201(2010), no. 1, 103128.Google Scholar
Chatyrko, V. and Kozlov, K., The maximal G-compactifications of G-spaces with special actions . In: Proceedings of the Ninth Prague Topological Symposium (2001), Topol. Atlas, North Bay, ON, 2002, pp. 1521.Google Scholar
Engelking, R., General topology. Second ed, Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989.Google Scholar
Kucharski, A., Plewik, Sz., and Valov, V., Skeletally Dugundji spaces . Central Eur. J. Math. 11(2013), 19491959.Google Scholar
Haydon, R., On a problem of Pelczynski: Milutin spaces, Dugundji spaces and AE(0–dim) . Studia Math. 52(1974), 2331. https://doi.org/10.4064/sm-52-1-23-31.Google Scholar
Mioduszewski, J. and Rudolf, L., H-closed and extremally disconnected Hausdorff spaces . Dissertationes Math. Rozprawy Mat. 66(1969).Google Scholar
Pełczyński, A., Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions . Dissert. Math. 58(1968), 189.Google Scholar
Sanchis, M. and Tkachenko, M., Totally Lindeöf and totally 𝜔-narrow semitopological groups . Topology Appl. 155(2008), no. 4, 322334. https://doi.org/10.1016/j.topol.2007.05.017.Google Scholar
Teleman, S., Sur la représentation linéaire des groupes topologiques . Ann. Sci. Ecole Norm. Sup. 74(1957), 319339. https://doi.org/10.24033/asens.1060.Google Scholar
Uspenskij, V., Topological groups and Dugundji compact spaces . (Russian) Mat. Sb. 180(1989), no. 8, 10921118. 1151.Google Scholar
Uspenskij, V., Compact quotient spaces of topological groups and Haydon spectra . (Russian) Mat. Zametki 42(1987), no. 4, 594602.Google Scholar
Veličko, N., A remark on plumed spaces . (Russian) Czechoslovak Math. J. 25(100)(1975), 819.Google Scholar