The equivariant universality and couniversality of the Cantor cube

Michael G. Megrelishvili; Tzvi Scarr

Fundamenta Mathematicae, Tome 167 (2001), p. 269-275 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $⟨ H ({0, 1}^{ℵ ₀}), {0, 1}^{ℵ ₀}, τ ⟩$ be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding $φ : G ↪ H ({0, 1}^{ℵ ₀})$ ; (2) there exists an embedding $ψ : X ↪ {0, 1}^{ℵ ₀}$ , equivariant with respect to φ, such that ψ(X) is an equivariant retract of ${0, 1}^{ℵ ₀}$ with respect to φ and ψ.

Publié le : 2001-01-01

Zbl 0967.54037

EUDML-ID : urn:eudml:doc:281728

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Michael G. Megrelishvili; Tzvi Scarr. The equivariant universality and couniversality of the Cantor cube. Fundamenta Mathematicae, Tome 167 (2001) pp. 269-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-3-4/