  Let $\sR$ be an epireflective category of $\topo$ and let $F_\sR$\, be the
epireflective functor associated with $\sR$. If $\sA$ denotes a
(semi)topological algebraic subcategory of $\topo$, we study when $F_\sR\,(A)$
is an epireflective subcategory of $\sA$. We prove that this is always the case
for semi-topological structures and we find some sufficient conditions for
topological algebraic structures. We also study when the epireflective functor
preserves products, subspaces and other properties. In particular, we solve an
open question about the coincidence of epireflections proposed by Echi and
Lazar in \cite[Question 1.6]{Echi:MPRIA} and repeated in \cite[Question
1.9]{Echi:TP}. Finally, we apply our results in different specific topological
algebraic structures.
