  \begin{abstrac} Let $(X,T) $ be a topological space, and $^{*}X$ a
non--standard extension of $X$. There is a natural ``standard'' topology
$^{S}T$ on $^{*}X$ generated by $^{*}G$, where $G\in T$. The topological space
$(^{*}X,^{S}T) $ will be used to study compactifications of $(X,T)$ in a
systematic way.
