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 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 کاملExtremal Pseudocompact Abelian Groups Are Compact Metrizable
Every pseudocompact Abelian group of uncountable weight has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology.
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Axioms
سال: 2016
ISSN: 2075-1680
DOI: 10.3390/axioms5010002