Without the restriction of metrizability, topological dynamical systems 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.
@article{bwmeta1.element.bwnjournal-article-fmv150i1p1bwm,
author = {Hong-Ting Shi and Hong-Wei Yang},
title = {Nonmetrizable topological dynamical characterization of central sets},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {1-9},
zbl = {0887.54036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i1p1bwm}
}
Shi, Hong-Ting; Yang, Hong-Wei. Nonmetrizable topological dynamical characterization of central sets. Fundamenta Mathematicae, Tome 149 (1996) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i1p1bwm/
[00000] [1] J. Auslander, Minimal Flows and their Extensions, North-Holland, Amsterdam, 1988. | Zbl 0654.54027
[00001] [2] V. Bergelson and N. Hindman, Nonmetrizable topological dynamics and Ramsey theory, Trans. Amer. Math. Soc. 320 (1990), 293-320. | Zbl 0725.22001
[00002] [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. | Zbl 0548.22002
[00003] [4] J. Berglund, H. Junghenn and P. Milnes, Analysis on Semigroups, Wiley, New York, 1989. | Zbl 0727.22001
[00004] [5] E. van Douwen, The Čech-Stone compactification of a discrete groupoid, Topology Appl. 39 (1991), 43-60. | Zbl 0758.54011
[00005] [6] R. Ellis, A semigroup associated with a transformation group, Trans. Amer. Math. Soc. 94 (1960), 272-281. | Zbl 0094.17402
[00006] [7] R. Ellis, Locally compact transformation groups, Duke Math. J. 24 (1957), 119-125. | Zbl 0079.16602
[00007] [8] R. Ellis, Lectures on Topological Dynamics, Benjamin, New York, 1969.
[00008] [9] R. Engelking, General Topology, Polish Scientific Publishers, Warszawa, 1977.
[00009] [10] Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87-91. | Zbl 0166.18602
[00010] [11] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorical Number Theory, Princeton University Press, Princeton, 1981.
[00011] [12] L. Gillman and M. Jerison, Rings of Continuous Functions, van Nostrand, Princeton, 1960. | Zbl 0093.30001
[00012] [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.