Discrete subsets and convergent sequences in topological groups

作者：Keyantuo Valentin; Zelenyuk Yevhen^*

来源：Topology and Its Applications, 2015, 191: 137-142.

DOI：10.1016/j.topol.2015.05.089

• Topological group
• Maximally almost periodic
• Totally bounded
• Extremally disconnected
• Discrete subset
• Convergent sequence
• Rapid ultrafilter
• P-point
• Selective ultafilter

We show that (1) assuming there is no rapid ultrafilter, every countable nondiscrete maximally almost periodic topological group contains a discrete nonclosed subset which is a convergent sequence in some weaker totally bounded group topology, (2) every infinite Abelian totally bounded topological group contains such a discrete subset (in ZFC), and (3) if an extremally disconnected topological group contains such a discrete subset, then there is a selective ultrafilter.

• 出版日期2015-8-15