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Simplicity of Categories Defined by Symmetry Axioms

Published online by Cambridge University Press:  20 November 2018

E. Lowen-Colebunders  and
Z. G. Szabo
E. Lowen-Colebunders
Affiliation:
Departement Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel
Z. G. Szabo
Affiliation:
Department for Analysis, L. Eötvös University Budapest, Muzeum krt 6-8, H-1088 Budapest
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Abstract

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We consider two generalizations R0w and R0 of the usual symmetry axiom for topological spaces to arbitrary closure spaces and convergence spaces. It is known that the two properties coincide on Top and define a non-simple subcategory. We show that R0W defines a simple subcategory of closure spaces and R0 a non-simple one. The last negative result follows from the stronger statement that every epireflective subcategory of R0 Conv containing all T1 regular topological spaces is not simple. Similar theorems are shown for the topological categories Fil and Mer.

Keywords

AMS (1980) Subject classification: 54A0554B30.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 240 - 248
Copyright
Copyright © Canadian Mathematical Society 1991

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