Hostname: page-component-7c8c6479df-5xszh Total loading time: 0 Render date: 2024-03-29T00:16:40.534Z Has data issue: false hasContentIssue false

Uniformities and uniformly continuous functions on locally connected groups

Published online by Cambridge University Press:  17 April 2009

Michael Megrelishvili (Levy)
Affiliation:
Department of Mathematics and Computer ScienceBar-Ilan University52900 Ramat-GanIsrael e-mail: megereli@bimacs.cs.biu.ac.il
Peter Nickolas
Affiliation:
Department of MathematicsUniversity of WollongongWollongong NSW 2522Australia e-mail: peter_nickolas@uow.edu.au
Vladimir Pestov
Affiliation:
Department of MathematicsVictoria University of WellingtonPO Box 600WellingtonNew Zealand e-mail: vladimir.pestov@vuw.ac.nz
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that the left and the right uniformities on a locally connected topological group G coincide if and only if every left uniformly continuous real-valued function on G is right uniformly continuous.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Hansell, G. and Troallic, J.P., ‘Sequential criteria for the equality of uniform structures in q-groups’, Topology Appl. 57 (1994), 4752.CrossRefGoogle Scholar
[2]Hernandez, S. and Sanchis, M., ‘Dugundji spaces in the coset space G/H’, in Papers on general topology and applications (Eighth Summer Conference At Queens College) (Annals New York Acad. Sci. 728, New York, 1994), pp. 262268.Google Scholar
[3]Hewitt, E. and Ross, K.A., Abstract harmonic analysis. Vol. 1 (Springer-Verlag, Berlin, Heidelberg, New York, 1979).CrossRefGoogle Scholar
[4]Itzkowitz, G., ‘Continuous measures, Baire category, and uniform continuity in topological groups’, Pacific J. Math. 54 (1974), 115125.CrossRefGoogle Scholar
[5]Itzkowitz, G., ‘Uniformities and uniform continuity on topological groups’, in General topology and applications (Staten Island, NY, 1989), Lecture Notes in Pure and Applied Mathematics 134 (Marcel-Dekker, New York, 1991), pp. 155178.Google Scholar
[6]Milnes, P., ‘Uniformity and uniformly continuous functions for locally compact groups’, Proc. Amer. Math. Soc. 109 (1990), 567570.CrossRefGoogle Scholar
[7]Protasov, I., ‘Functionally balanced groups’, Math. Notes 49 6 (1991), 614616.CrossRefGoogle Scholar
[8]Roelcke, W. and Dierolf, S., Uniform structures in topological groups and their quotients (McGraw-Hill, New York, 1981).Google Scholar