Chains of pseudocompact group topologies
نویسندگان
چکیده
منابع مشابه
Imposing pseudocompact group topologies on Abelian groups
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. We show: Theorem 3.3. Among groups of cardinality γ, the group ⊕γQ serves as a “test space” for the availability of a pseudocompact group topology in this sense: If m(α) ≤ γ ≤ 2 then ⊕γQ admits a (necessarily connect...
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P is the class of pseudocompact Hausdorff topological groups, and P′ is the class of groups which admit a topology T such that (G,T ) ∈ P. It is known that every G= (G,T ) ∈ P is totally bounded, so for G ∈ P′ the supremum T ∨(G) of all pseudocompact group topologies on G and the supremum T #(G) of all totally bounded group topologies on G satisfy T ∨ ⊆ T #. The authors conjecture for abelian G...
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We show that every Abelian group satisfying a mild cardinal inequality admits a pseudocompact group topology from which all countable subgroups inherit the maximal totally bounded topology (we say that such a topology satisfies property ♯). This criterion is used in conjunction with an analysis of the algebraic structure of pseudocompact groups to obtain, under the Generalized Continuum Hypothe...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1998
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(96)00110-7