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Minimal actions on Cantor cubes

Turek S.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 2

129-138

There are investigated minimal actions of countable groups on the Cantor cube of weight continuum. In particular there is shown that for every countable abelian group G there exists a homomorphism pi of G into the group Homeo(D^2omega) of all homeomorphisms of the Cantor cube D^2omega onto itself such that for every x is a member of a set D^2omega the orbit {pi{g)(x):g is a member of a set G} is dense in the cube.