A note on universal minimal dynamical systems

Sławomir Turek

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 4, page 781-783
  • ISSN: 0010-2628

Abstract

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Let M ( G ) denote the phase space of the universal minimal dynamical system for a group G . Our aim is to show that M ( G ) is homeomorphic to the absolute of D 2 ω , whenever G is a countable Abelian group.

How to cite

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Turek, Sławomir. "A note on universal minimal dynamical systems." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 781-783. <http://eudml.org/doc/247298>.

@article{Turek1991,
abstract = {Let $M(G)$ denote the phase space of the universal minimal dynamical system for a group $G$. Our aim is to show that $M(G)$ is homeomorphic to the absolute of $D^\{2^\omega \}$, whenever $G$ is a countable Abelian group.},
author = {Turek, Sławomir},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {dynamical system; universal minimal dynamical system; Abelian group; absolute; universal minimal dynamical system; absolute of },
language = {eng},
number = {4},
pages = {781-783},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on universal minimal dynamical systems},
url = {http://eudml.org/doc/247298},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Turek, Sławomir
TI - A note on universal minimal dynamical systems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 4
SP - 781
EP - 783
AB - Let $M(G)$ denote the phase space of the universal minimal dynamical system for a group $G$. Our aim is to show that $M(G)$ is homeomorphic to the absolute of $D^{2^\omega }$, whenever $G$ is a countable Abelian group.
LA - eng
KW - dynamical system; universal minimal dynamical system; Abelian group; absolute; universal minimal dynamical system; absolute of
UR - http://eudml.org/doc/247298
ER -

References

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  1. Balcar B., Błaszczyk A., On minimal dynamical systems on Boolean algebras, Comment. Math. Univ. Carolinae 31 (1990), 7-11. (1990) MR1056164
  2. Comfort W.W., Topological Groups, Handbook of set-theoretic topology, North-Holland, 1984, 1143-1260. Zbl1071.54019MR0776643
  3. van Douwen E.K., The maximal totally bounded group topology on G and the biggest minimal G -space, for Abelian groups G , Topology and its Appl. 34 (1990), 69-91. (1990) Zbl0696.22003MR1035461
  4. Ellis R., Lectures on Topological Dynamics, Benjamin, New York, 1969 (). Zbl0193.51502MR0267561
  5. Hewitt E., Ross K.A., Abstract Harmonic Analysis I, Springer, Berlin, 1963. 
  6. van der Woude J., Topological Dynamix, Mathematisch Centrum, Amsterdam, 1982. Zbl0654.54026

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