منابع مشابه
Non-Abelian Pseudocompact Groups
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...
متن کاملImposing 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...
متن کاملExtremal 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.
متن کاملA note on quasi irresolute topological groups
In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...
متن کاملExtremal pseudocompact Abelian groups : A unified treatment
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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1989
ISSN: 0002-9939
DOI: 10.2307/2047849