- Tytuł:
- Imposing psendocompact group topologies on Abeliau groups
- Autorzy:
-
Comfort, W.
Remus, I. - Powiązania:
- https://bibliotekanauki.pl/articles/1208627.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
pseudocompact group
$G_δ$-dense subgroup
singular cardinals hypothesis
torsion-free rank
connected topological group
0-dimensional group
divisible hull
chain
anti-chain - Opis:
-
The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, $m(α) ≤ 2^α$. We show:
Theorem 4.12. Let G be Abelian with |G| = γ. If either m(α) ≤ α and m$(α)≤ r_0 (G) ≤ γ ≤ 2^α$, or α > ω and $α^ω ≤ r_0(G) ≤ 2^α$, then G admits a pseudocompact group topology of weight α.
Theorem 4.15. Every connected, pseudocompact Abelian group G with wG = α ≥ ω satisfies $r_0(G) ≥ m(α)$.
Theorem 5.2(b). If G is divisible Abelian with $2^{r_{0}(G)} ≤ γ$, then G admits at most $2^γ$-many pseudocompact group topologies.
Theorem 6.2. Let $β = α^ω$ or $β = 2^α$ with β ≥ α, and let $β ≤ γ < κ ≤ 2^β$. Then both $⊕_γℚ$ and the free Abelian group on γ-many generators admit exactly $2^κ$-many pseudocompact group topologies of weight κ. Of these, some $κ^+$-many form a chain and some $2^κ$-many form an anti-chain. - Źródło:
-
Fundamenta Mathematicae; 1993, 142, 3; 221-240
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł