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Imposing psendocompact group topologies on Abeliau groups

W. ComfortI. Remus — 1993

Fundamenta Mathematicae

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...

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