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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 R 0w and R 0 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 T 1 regular topological spaces is not simple. Similar theorems are shown for the topological categories Fil and Mer.

Keywords

AMS (1980) Subject classification: 54A0554B30.

Information

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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