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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the nonsimplicity of some convergence categories


Authors: E. Lowen and R. Lowen
Journal: Proc. Amer. Math. Soc. 105 (1989), 305-308
MSC: Primary 18B99; Secondary 54A25, 54B30
DOI: https://doi.org/10.1090/S0002-9939-1989-0936777-1
MathSciNet review: 936777
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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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DOI: https://doi.org/10.1090/S0002-9939-1989-0936777-1
Article copyright: © Copyright 1989 American Mathematical Society