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1996 | 150 | 1 | 1-9
Tytuł artykułu

Nonmetrizable topological dynamical characterization of central sets

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Without the restriction of metrizability, topological dynamical systems $(X,⟨ T_s⟩_{s ∈ G})$ 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.
Rocznik
Tom
150
Numer
1
Strony
1-9
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-03-16
poprawiono
1995-11-21
Twórcy
  • Department of Mathematics, Capital Normal University, Beijing, 00037, P. R. China
  • Department of Mathematics, Capital Normal University, Beijing, 00037, P. R. China
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv150i1p1bwm
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