Geodesic
Simplicity of Categories Defined by Symmetry Axioms
Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 240-248

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DOI

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.
DOI : 10.4153/CMB-1991-039-0
Mots-clés : AMS (1980) Subject classification: 54A05, 54B30. 
Lowen-Colebunders, E.; Szabo, Z. G. Simplicity of Categories Defined by Symmetry Axioms. Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 240-248. doi: 10.4153/CMB-1991-039-0
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     author = {Lowen-Colebunders, E. and Szabo, Z. G.},
     title = {Simplicity of {Categories} {Defined} by {Symmetry} {Axioms}},
     journal = {Canadian mathematical bulletin},
     pages = {240--248},
     year = {1991},
     volume = {34},
     number = {2},
     doi = {10.4153/CMB-1991-039-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-039-0/}
}
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