Geodesic
Productivity of coreflective classes of topological groups
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 551-560 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Every nontrivial countably productive coreflective subcategory of topological linear spaces is $\kappa$-productive for a large cardinal $\kappa$ (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal $\kappa$, there are coreflective subcategories that are $\kappa$-productive and not $\kappa^+$-productive (see [8]). From certain points of view, the category of topological groups lies in between those categories above and we shall show that the corresponding results on productivity of coreflective subcategories are also ``in between'': for some coreflections the results analogous to those in topological linear spaces are true, for others the results analogous to those for uniform spaces hold.
Every nontrivial countably productive coreflective subcategory of topological linear spaces is $\kappa$-productive for a large cardinal $\kappa$ (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal $\kappa$, there are coreflective subcategories that are $\kappa$-productive and not $\kappa^+$-productive (see [8]). From certain points of view, the category of topological groups lies in between those categories above and we shall show that the corresponding results on productivity of coreflective subcategories are also ``in between'': for some coreflections the results analogous to those in topological linear spaces are true, for others the results analogous to those for uniform spaces hold.
Classification : 18A40, 18B30, 54B10, 54B30, 54H11
Keywords: productivity; topological group; coreflective class 
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     title = {Productivity of coreflective classes of topological groups},
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Herrlich, Horst; Hušek, Miroslav. Productivity of coreflective classes of topological groups. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 551-560. http://geodesic.mathdoc.fr/item/CMUC_1999_40_3_a13/