Previous |  Up |  Next


dynamical system; universal minimal dynamical system; Abelian group; absolute
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.
[1] Balcar B., Błaszczyk A.: On minimal dynamical systems on Boolean algebras. Comment. Math. Univ. Carolinae 31 (1990), 7-11. MR 1056164
[2] Comfort W.W.: Topological Groups. Handbook of set-theoretic topology, North-Holland, 1984, 1143-1260. MR 0776643 | Zbl 1071.54019
[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. MR 1035461 | Zbl 0696.22003
[4] Ellis R.: Lectures on Topological Dynamics. Benjamin, New York, 1969 (). MR 0267561 | Zbl 0193.51502
[5] Hewitt E., Ross K.A.: Abstract Harmonic Analysis I. Springer, Berlin, 1963.
[6] van der Woude J.: Topological Dynamix. Mathematisch Centrum, Amsterdam, 1982. Zbl 0654.54026
Partner of
EuDML logo