Selectively Pseudocompact Groups without Infinite Separable Pseudocompact Subsets
نویسندگان
چکیده
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...
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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...
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 کاملConcerning Connected, Pseudocompact Abelian Groups
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...
متن کاملPseudocompact 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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ژورنال
عنوان ژورنال: Axioms
سال: 2018
ISSN: 2075-1680
DOI: 10.3390/axioms7040086