2011
DOI: 10.1515/9783110258356
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Algebra in the Stone-Cech Compactification

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Cited by 281 publications
(725 citation statements)
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“…We denote the minimal ideal by K. In what follows, we apply the fact that K is the union of all minimal left ideals of G LU C (see [HS,p. 34]).…”
Section: Uniform Compactifications Of Subspacesmentioning
confidence: 99%
“…We denote the minimal ideal by K. In what follows, we apply the fact that K is the union of all minimal left ideals of G LU C (see [HS,p. 34]).…”
Section: Uniform Compactifications Of Subspacesmentioning
confidence: 99%
“…With this operation, βW becomes a compact Hausdorff right topological semigroup; in particular, the map p → pq is continuous for each q ∈ βW . See [7] for full details.…”
Section: Applicationsmentioning
confidence: 99%
“…The largest semigroup compactification of G with the joint continuity property, in the sense that any other is a natural quotient, is called the LU C-compactification and denoted by G LU C . The homomorphism ψ : G → G LU C is a topological embedding, so we identify G with its image, and write G * = G LU C \ G. As a topological compactification, G LU C is characterized by the property that a continuous function f : G → [0, 1] extends to a continuous functionf : G LU C → [0, 1] if and only if f is uniformly continuous with respect to the right uniformity (see [2,Theorem 21.41]). If G is locally compact, then every semigroup compactification of G has the joint continuity property (see [8,Theorem II.4.3]), so G LU C is the largest semigroup compactification of G. In the case, where G is discrete, G LU C coincides with βG, the Stone-Čech compactification.…”
Section: Introductionmentioning
confidence: 99%
“…Example 1.3. Let Z (2) denote the additive group of 2-adic integers and let H = ω Z (2) . Define the subgroups K and G of H by K = 2H = ω 2Z (2) and G = ω Z (2) + K. Define the group topology on G by taking the natural compact topology on K and declaring the subgroup K to be open.…”
Section: Introductionmentioning
confidence: 99%
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