Epireflections in topological algebraic structures
arXiv:1704.01146
Abstract
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.