On the nonsimplicity of some convergence categories

Abstract

The category TOP of topological spaces is known to be Convsimple in the sense that there exists a single object E E in Top such that Top is the epireflective hull of { E } \left \{ E \right \} in the category Conv of convergence spaces. Prtop, the category of pretopological spaces is also Conv-simple. We show that on the contrary the category Pstop of pseudo topological spaces and Conv itself are not Conv-simple. More specifically every epireflective subcategory of Conv which contains all Hausdorff c c -embedded locally compact spaces is not Conv-simple.