منابع مشابه
Extremal α-pseudocompact abelian groups
Let α be an infinite cardinal. Generalizing a recent result of Comfort and van Mill, we prove that every α-pseudocompact abelian group of weight > α has some proper dense α-pseudocompact subgroup and admits some strictly finer α-pseudocompact group topology. AMS classification numbers: Primary 22B05, 22C05, 40A05; Secondary 43A70, 54A20.
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Every pseudocompact Abelian group of uncountable weight has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology.
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The authors have shown [Proc. Amer. Math. Soc. 135 (2007), 4039– 4044] that every nonmetrizable, pseudocompact abelian group has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology. Here they give a comprehensive, direct and self-contained proof of this result.
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In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class N of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces N that gives some new examples...
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Here are three recently-established theorems from the literature. (A) (2006) Every non-metrizable compact abelian group K has 2|K|-many proper dense pseudocompact subgroups. (B) (2003) Every non-metrizable compact abelian group K admits 22 |K| -many strictly finer pseudocompact topological group refinements. (C) (2007) Every non-metrizable pseudocompact abelian group has a proper dense pseudoco...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2005
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2004.08.018