Minimal dynamical system for \(\omega\)-bounded groups. (English) Zbl 0831.54035

Turek, S.

Acta Univ. Carol., Math. Phys. 35, No. 2, 77-81 (1994).

A topological group is \(\omega\)-bounded if for any open neighbourhood \(V\) of the identity element there is a countable set \(F \subseteq G\) such that \(G = FV\). Topological spaces are called coabsolute if their Boolean algebras of regular open subsets are isomorphic. The author gives a direct proof of the following theorem (due to Bandlow): If \((G, X, \pi)\) is a minimal dynamical system and \(G\) is \(\omega\)-bounded then \(X\) is coabsolute to the Cantor cube \(D^\tau\) for some cardinal \(\tau\).

Reviewer: T.S.Wu (Cleveland)

MSC:

54H20

Topological dynamics (MSC2010)

Keywords:

coabsolute space