Relativized problems with abelian phase group in topological dynamics

AUTOR(ES)

McMahon, Douglas

RESUMO

Let (X, T) be the equicontinuous minimal transformation group with X = π∞Z2, the Cantor group, and S = [unk]∞Z2 endowed with the discrete topology acting on X by right multiplication. For any countable group T we construct a function F:X × S → T such that if (Y, T) is a minimal transformation group, then (X × Y, S) is a minimal transformation group with the action defined by (x, y)s = [xs, yF(x, s)]. If (W, T) is a minimal transformation group and ϕ:(Y, T) → (W, T) is a homomorphism, then identity x ϕ:(X × Y, S) → (X × W, S) is a homomorphism and has many of the same properties that ϕ has. For this reason, one may assume that the phase group is abelian (or S) without loss of generality for many relativized problems in topological dynamics.

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