Speaker: Yevhen Zelenyuk (Wits. University)

Title: Discontinuity of multiplication and left translations in $G^{LUC}$

Abstract: Every locally compact group $G$ has a largest semigroup
compactification, denoted $G^{LUC}$. For every $p\in G$ and $q\in G^{LUC}$,
the multiplication in $G^{LUC}$ is continuous at $(p,q)$ (Ellis 1957), and
for every $p\in G^*=G^{LUC}\setminus G$, the left translation by $p$ in
$G^*$ is discontinuous (Protasov and Pym 2001). We shall discuss the
question whether there are $p,q\in G^*$ such that the multiplication in
$G^{LUC}$ is continuous at $(p,q)$ or the left translation by $p$ in $G^*$
is continuous at $q$.