Geodesic
Topologies on groups determined by right cancellable ultrafilters
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 1, pp. 135-139 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 54C05, 54G15, 54H11
Keywords: Stone-Čech compactification; right cancellable ultrafilters; left invariant topologies 
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     author = {Protasov, I. V.},
     title = {Topologies on groups determined by right cancellable ultrafilters},
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     pages = {135--139},
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     zbl = {1212.54101},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2009_50_1_a11/}
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Protasov, I. V. Topologies on groups determined by right cancellable ultrafilters. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 1, pp. 135-139. http://geodesic.mathdoc.fr/item/CMUC_2009_50_1_a11/