The equivariant universality and couniversality of the Cantor cube

• Autorzy: Michael G. Megrelishvili , Tzvi Scarr
• Języki publikacji: EN

Abstrakty

EN

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 $⟨H({0,1}^{ℵ₀}),{0,1}^{ℵ₀},τ⟩$ be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then
(1) there exists a topological group embedding $φ: G ↪ H({0,1}^{ℵ₀})$;
(2) there exists an embedding $ψ: X ↪ {0,1}^{ℵ₀}$, equivariant with respect to φ, such that ψ(X) is an equivariant retract of ${0,1}^{ℵ₀}$ with respect to φ and ψ.

Kategorie tematyczne

• 22A99: None of the above, but in this section
• 54H15: Transformation groups and semigroups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 167
• Numer: 3
• Strony: 269-275

Daty

wydano

2001

Twórcy

autor

Michael G. Megrelishvili

• Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel

autor

Tzvi Scarr

• Department of Applied Mathematics, Jerusalem College of Technology, 21 Havaad Haleumi St., Jerusalem, Israel 91160

Identyfikatory

DOI

10.4064/fm167-3-4