Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T11:11:42.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximally highly proximal generators of minimal flows

Published online by Cambridge University Press:  19 September 2008

Joseph Auslander  and
Jaap van der Woude
Joseph Auslander
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA; and Stichting Mathematisch Centrum, Amsterdam, The Netherlands
Jaap van der Woude
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA; and Stichting Mathematisch Centrum, Amsterdam, The Netherlands
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 study minimal flows and their extensions by means of the associated maximally highly proximal flows. These, in turn, can be represented by highly proximal generators, which are certain subsets of the universal minimal flow. From this point of view we obtain information on relative disjointness, coalescence, the Bronstein property, and RIC extensions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 4 , December 1981 , pp. 389 - 412
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

[1]Armstrong, T. E.. Gleason spaces and topological dynamics. Indiana Math. J. 27 (1978), 283–292.CrossRefGoogle Scholar
[2]Auslander, J.. Regular minimals sets, I. Trans Amer. Math. Soc. 123 (1966), 469–479.CrossRefGoogle Scholar
[3]Auslander, J. & Glasner, S.. Distal and highly proximal extensions of minimal flows. Indiana Math. J. 26 (1900), 731–749.CrossRefGoogle Scholar
[4]Comfort, W. W.. Ultrafilters: some old and new results. Bull. Amer. Math. Soc. 83 (1977), 417–455.CrossRefGoogle Scholar
[5]Ellis, R.. Lectures on Topological Dynamics. W. A. Benjamin: New York, 1969.Google Scholar
[6]Ellis, R.. The Furstenberg structure theorem. Pacific J. Math. 76 (1978), 345–349.CrossRefGoogle Scholar
[7]Glasner, S.. Proximal Flows. Lecture Notes in Math. 517. Springer-Verlag: Berlin, 1976.CrossRefGoogle Scholar
[8]McMahon, D. C. & Wu, T. S.. On the connectedness of homomorphisms in topological dynamics. Trans. Amer. Math. Soc. 217 (1976), 257–270.CrossRefGoogle Scholar
[9]Parry, W. & Walters, P.. Minimal skew product homeomorphisms and coalescence. Compositio Math. 22 (1970), 283–288.Google Scholar
[10]Veech, W. A.. Topological dynamics. Bull. Amer. Math. Soc. 83 (1977), 775–830.CrossRefGoogle Scholar
[11]Willard, S.. General Topology. Addison Wesley: Reading, Mass., 1970.Google Scholar