Advanced Search

Let ⟨G,X,α⟩ be a G-space, where G is a non-Archimedean (having a local base at the identity consisting of open subgroups) and second countable topological group, and X is a zero-dimensional compact metrizable space. Let $⟨H\left({0,1}^{\aleph ₀}\right),{0,1}^{\aleph ₀},\tau ⟩$ be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding $\phi :G\hookrightarrow H\left({0,1}^{\aleph ₀}\right)$; (2) there exists an embedding $\psi :X\hookrightarrow {0,1}^{\aleph ₀}$, equivariant with respect to φ, such that ψ(X) is an equivariant retract of ${0,1}^{\aleph ₀}$ with respect to φ...