Abelian groups admitting a Fréchet–Urysohn pseudocompact topological group topology
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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It is known that if P is either the property w-bounded or countably compact, then for every cardinal a 2 w there is a P-group G such that H.G = a and no proper, dense subgroup of G is a P-group. What happens when P is the property pseudocompact? The first-listed author and Robertson have shown that every zero-dimensional Abelian P-group G with H.G > o has a proper, dense, P-group. Turning to th...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2010
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2009.09.016