Almost maximal topologies on groups
Tom 234 / 2016
Fundamenta Mathematicae 234 (2016), 91-100
MSC: Primary 22A15, 54G05; Secondary 54D80, 54H11.
DOI: 10.4064/fm150-12-2015
Opublikowany online: 2 March 2016
Streszczenie
Let $G$ be a countably infinite group. We show that for every finite absolute coretract $S$, there is a regular left invariant topology on $G$ whose ultrafilter semigroup is isomorphic to $S$. As consequences we prove that (1) there is a right maximal idempotent in $\beta G\setminus G$ which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination $(-,-,+)$, there is a corresponding regular almost maximal left invariant topology on $G$.