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2 Bulletin of the Polish Academy of Sciences. Mathematics

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An isomorphic classification of C(2m x [0, α]) spaces

Galego E. M.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

Vol. 57, no 3-4

279-287

We present an extension of the classical isomorphic classification of the Banach spaces C([0, α]) of all real continuous functions defined on the nondenumerable intervals of ordinals [0, α]. As an application, we establish the isomorphic classification of the Banach spaces C(2m x [0, α]) of all real continuous functions defined on the compact spaces 2m x [0, α], the topological product of the Cantor cubes 2m with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, α]. Consequently, it is relatively consistent with ZFC that this yields a complete isomorphic classification of C(2m x [0, α]) spaces.

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.