# The equivariant universality and couniversality of the Cantor cube

Michael G. Megrelishvili; Tzvi Scarr

Fundamenta Mathematicae (2001)

- Volume: 167, Issue: 3, page 269-275
- ISSN: 0016-2736

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topMichael G. Megrelishvili, and Tzvi Scarr. "The equivariant universality and couniversality of the Cantor cube." Fundamenta Mathematicae 167.3 (2001): 269-275. <http://eudml.org/doc/281728>.

@article{MichaelG2001,

abstract = {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.},

author = {Michael G. Megrelishvili, Tzvi Scarr},

journal = {Fundamenta Mathematicae},

keywords = {Cantor cube; -compactification; universal space; non-Archimedean group},

language = {eng},

number = {3},

pages = {269-275},

title = {The equivariant universality and couniversality of the Cantor cube},

url = {http://eudml.org/doc/281728},

volume = {167},

year = {2001},

}

TY - JOUR

AU - Michael G. Megrelishvili

AU - Tzvi Scarr

TI - The equivariant universality and couniversality of the Cantor cube

JO - Fundamenta Mathematicae

PY - 2001

VL - 167

IS - 3

SP - 269

EP - 275

AB - 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.

LA - eng

KW - Cantor cube; -compactification; universal space; non-Archimedean group

UR - http://eudml.org/doc/281728

ER -

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