Article

 Title: Productivity of coreflective classes of topological groups (English) Author: Herrlich, Horst Author: Hušek, Miroslav Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 40 Issue: 3 Year: 1999 Pages: 551-560 . Category: math . Summary: 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. (English) Keyword: productivity Keyword: topological group Keyword: coreflective class MSC: 18A40 MSC: 18B30 MSC: 54B10 MSC: 54B30 MSC: 54H11 idZBL: Zbl 1009.54041 idMR: MR1732481 . Date available: 2009-01-08T18:55:09Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/119110 . Reference: [1] Adámek J., Herrlich H., Strecker G.: Abstract and Concrete Categories.Wiley Interscience, New York, 1990. MR 1051419 Reference: [2] Balcar B: Sequential Boolean algebras.preprint, May 1995. Reference: [3] Balcar B., Hušek M.: Sequential continuity and submeasurable cardinals.to appear in Topology Appl. MR 1806027 Reference: [4] Chudnovskij D.V.: Sequentially continuous mappings and real-valued measurable cardinals.Infinite and finite sets (Colloq. Math. Soc. J. Bolyai, Vol.10, Part I, Keszthély 1973), (North Holland, Amsterdam, 1975), pp.275-288. MR 0505507 Reference: [5] Dierolf S.: Über asoziirte lineare und lokalkonvexe Topologien.Manuscripta Math. 16 (1975), 27-46. MR 0415351 Reference: [6] Dierolf P., Dierolf S.: On linear topologies determined by a family of subsets of a topological vector spaces.Gen. Topology Appl. 8 (1978), 127-140. MR 0473867 Reference: [7] Herrlich H.: On the concept of reflections in general topology.in: Contributions to Extension Theory of Topological Structures, Proc. Symp. Berlin 1967 (VEB, Berlin 1969). Zbl 0182.25301, MR 0284986 Reference: [8] Hušek M.: Products of uniform spaces.Czech. Math. J. 29 (1979), 130-141. MR 0518147 Reference: [9] Hušek M.: Sequentially continuous homomorphisms on products of topological groups.Topology Appl. 70 (1996), 155-165. MR 1397074 Reference: [10] Hušek M.: Productivity of some classes of topological linear spaces.Topology Appl. 80 (1997), 141-154. MR 1469474 Reference: [11] Semadeni Z., Swirszcz T.: Reflective and coreflective subcategories of categories of Banach spaces and Abelian groups.Bull. Acad. Pol. 25 (1977), 1105-1107. MR 0476824 Reference: [12] Shelah S.: Infinite Abelian groups, Whitehead problem and some constructions.Israel J. Math. 18 (1974), 243-256. Zbl 0318.02053, MR 0357114 Reference: [13] Solovay R.M.: Real-valued measurable cardinals.Axiomatic Set Theory (Proc. Symp. Pure Math., Vol XIII, Part I, California, 1967, Amer. Math. Soc., 1971), pp.397-428. Zbl 0222.02078, MR 0290961 Reference: [14] Sydow W.: Über die Kategorie der topologischen Vektorräume.Doktor-Dissertation (Fernuniversität Hagen, 1980). Zbl 0466.18006 .

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