Extremal Pseudocompact Abelian Groups Are Compact Metrizable
نویسندگان
چکیده
Every pseudocompact Abelian group of uncountable weight has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology.
منابع مشابه
Pseudocompact groups : progress and problems ✩
Several months ago the speaker and Jan van Mill gave a proof of this result [W.W. Comfort, J. van Mill, Extremal pseudocompact abelian groups are compact metrizable, Abstracts Amer. Math. Soc. 27 (2006) 78 (Abstract #1014-22-958); W.W. Comfort, J. van Mill, Extremal pseudocompact abelian groups are compact metrizable, Proc. Amer. Math. Soc. 135 (2007) 4039–4044]: A pseudocompact abelian group o...
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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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تاریخ انتشار 2007