On the nonsimplicity of some convergence categories

Lowen, E.; Lowen, R.

doi:10.1090/S0002-9939-1989-0936777-1

On the nonsimplicity of some convergence categories
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Proc. Amer. Math. Soc. 105 (1989), 305-308 Request permission

Abstract:

The category TOP of topological spaces is known to be Convsimple in the sense that there exists a single object $E$ in Top such that Top is the epireflective hull of $\left \{ E \right \}$ 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 $c$-embedded locally compact spaces is not Conv-simple.

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Rechts-Bikategoriestrukturen in topologischen Kategorien