Locally Minimal Topological Groups 2

Details Locally Minimal Topological Groups 2 Locally Minimal Topological Groups 2

2010-06-28

arxiv.org/abs/1006.5285v1

Mathematics

General Topology

Scientific paper

We continue in this paper the study of locally minimal groups started in \cite{LocMin}. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian groups containing dense countable locally minimal subgroups, as well as those containing dense locally minimal subgroups of countable free-rank. We also characterize the compact abelian groups whose torsion part is dense and locally minimal. We call a topological group $G$ {\it almost minimal} if it has a closed, minimal normal subgroup $N$ such that the quotient group $G/N$ is uniformly free from small subgroups. The class of almost minimal groups includes all locally compact groups, and is contained in the class of locally minimal groups. On the other hand, we provide examples of countable precompact metrizable locally minimal groups which are not almost minimal. Some other significant properties of this new class are obtained.

Affiliated with

Also associated with

No associations

Rating

Locally Minimal Topological Groups 2 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Locally Minimal Topological Groups 2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Locally Minimal Topological Groups 2 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-616157