Download PDF - Nonmetrizable topological dynamical characterization of central setsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Nonmetrizable topological dynamical characterization of central sets

Authors 1, 1

Affiliations

  1. Department of Mathematics, Capital Normal University, Beijing, 00037, P. R. China

Abstract

Without the restriction of metrizability, topological dynamical systems (X,⟨Ts⟩s∈G) are defined and uniform recurrence and proximality are studied. Some well known results are generalized and some new results are obtained. In particular, a topological dynamical characterization of central sets in an arbitrary semigroup (G,+) is given and shown to be equivalent to the usual algebraic characterization.

Keywords

ENG
topological dynamical system, enveloping semigroup, uniform recurrence, proximality, minimal idempotent, central subset

Bibliography

  1. J. Auslander, Minimal Flows and their Extensions, North-Holland, Amsterdam, 1988.
  2. V. Bergelson and N. Hindman, Nonmetrizable topological dynamics and Ramsey theory, Trans. Amer. Math. Soc. 320 (1990), 293-320.
  3. J. Berglund and N. Hindman, Filters and the weak almost periodic compactification of a discrete semigroup, Trans. Amer. Math. Soc. 284 (1984), 1-38.
  4. J. Berglund, H. Junghenn and P. Milnes, Analysis on Semigroups, Wiley, New York, 1989.
  5. E. van Douwen, The Čech-Stone compactification of a discrete groupoid, Topology Appl. 39 (1991), 43-60.
  6. R. Ellis, A semigroup associated with a transformation group, Trans. Amer. Math. Soc. 94 (1960), 272-281.
  7. R. Ellis, Locally compact transformation groups, Duke Math. J. 24 (1957), 119-125.
  8. R. Ellis, Lectures on Topological Dynamics, Benjamin, New York, 1969.
  9. R. Engelking, General Topology, Polish Scientific Publishers, Warszawa, 1977.
  10. Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87-91.
  11. H. Furstenberg, Recurrence in Ergodic Theory and Combinatorical Number Theory, Princeton University Press, Princeton, 1981.
  12. L. Gillman and M. Jerison, Rings of Continuous Functions, van Nostrand, Princeton, 1960.
  13. N. Hindman, Ultrafilters and Ramsey Theory - an update, in: Set Theory and its Applications, J. Steprāns and S. Watson (eds.), Lecture Notes in Math. 1401, Springer, 1989, 97-118.
Fundamenta Mathematicae
1996/150/1
Export to PBN, Opens in new tab
Pages:
1-9
Main language of publication
English
Received
1995-03-16
Accepted
1995-11-21
Published
1996
Exact and natural sciences