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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:
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 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 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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