Topologies on groups determined by right cancellable ultrafilters

Protasov, Igor V.. "Topologies on groups determined by right cancellable ultrafilters." Commentationes Mathematicae Universitatis Carolinae 50.1 (2009): 135-139. <http://eudml.org/doc/32487>.

@article{Protasov2009,
abstract = {For every discrete group $G$, the Stone-Čech compactification $\beta G$ of $G$ has a natural structure of a compact right topological semigroup. An ultrafilter $p\in G^*$, where $G^*=\beta G\setminus G$, is called right cancellable if, given any $q,r\in G^*$, $qp=rp$ implies $q=r$. For every right cancellable ultrafilter $p\in G^*$, we denote by $G(p)$ the group $G$ endowed with the strongest left invariant topology in which $p$ converges to the identity of $G$. For any countable group $G$ and any right cancellable ultrafilters $p,q\in G^*$, we show that $G(p)$ is homeomorphic to $G(q)$ if and only if $p$ and $q$ are of the same type.},
author = {Protasov, Igor V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Stone-Čech compactification; right cancellable ultrafilters; left invariant topologies; Stone-Čech compactification; right cancellable ultrafilter; left invariant topology},
language = {eng},
number = {1},
pages = {135-139},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Topologies on groups determined by right cancellable ultrafilters},
url = {http://eudml.org/doc/32487},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Protasov, Igor V.
TI - Topologies on groups determined by right cancellable ultrafilters
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 1
SP - 135
EP - 139
AB - For every discrete group $G$, the Stone-Čech compactification $\beta G$ of $G$ has a natural structure of a compact right topological semigroup. An ultrafilter $p\in G^*$, where $G^*=\beta G\setminus G$, is called right cancellable if, given any $q,r\in G^*$, $qp=rp$ implies $q=r$. For every right cancellable ultrafilter $p\in G^*$, we denote by $G(p)$ the group $G$ endowed with the strongest left invariant topology in which $p$ converges to the identity of $G$. For any countable group $G$ and any right cancellable ultrafilters $p,q\in G^*$, we show that $G(p)$ is homeomorphic to $G(q)$ if and only if $p$ and $q$ are of the same type.
LA - eng
KW - Stone-Čech compactification; right cancellable ultrafilters; left invariant topologies; Stone-Čech compactification; right cancellable ultrafilter; left invariant topology
UR - http://eudml.org/doc/32487
ER -