Productivity of coreflective classes of topological groups
Horst Herrlich; Miroslav Hušek
Commentationes Mathematicae Universitatis Carolinae (1999)
- Volume: 40, Issue: 3, page 551-560
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topHerrlich, Horst, and Hušek, Miroslav. "Productivity of coreflective classes of topological groups." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 551-560. <http://eudml.org/doc/248434>.
@article{Herrlich1999,
abstract = {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.},
author = {Herrlich, Horst, Hušek, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {productivity; topological group; coreflective class; topological group; productivity; coreflective class},
language = {eng},
number = {3},
pages = {551-560},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Productivity of coreflective classes of topological groups},
url = {http://eudml.org/doc/248434},
volume = {40},
year = {1999},
}
TY - JOUR
AU - Herrlich, Horst
AU - Hušek, Miroslav
TI - Productivity of coreflective classes of topological groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 551
EP - 560
AB - 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.
LA - eng
KW - productivity; topological group; coreflective class; topological group; productivity; coreflective class
UR - http://eudml.org/doc/248434
ER -
References
top- Adámek J., Herrlich H., Strecker G., Abstract and Concrete Categories, Wiley Interscience, New York, 1990. MR1051419
- Balcar B, Sequential Boolean algebras, preprint, May 1995.
- Balcar B., Hušek M., Sequential continuity and submeasurable cardinals, to appear in Topology Appl. MR1806027
- 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. MR0505507
- Dierolf S., Über asoziirte lineare und lokalkonvexe Topologien, Manuscripta Math. 16 (1975), 27-46. (1975) MR0415351
- 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. (1978) MR0473867
- 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). Zbl0182.25301MR0284986
- Hušek M., Products of uniform spaces, Czech. Math. J. 29 (1979), 130-141. (1979) MR0518147
- Hušek M., Sequentially continuous homomorphisms on products of topological groups, Topology Appl. 70 (1996), 155-165. (1996) MR1397074
- Hušek M., Productivity of some classes of topological linear spaces, Topology Appl. 80 (1997), 141-154. (1997) MR1469474
- Semadeni Z., Swirszcz T., Reflective and coreflective subcategories of categories of Banach spaces and Abelian groups, Bull. Acad. Pol. 25 (1977), 1105-1107. (1977) MR0476824
- Shelah S., Infinite Abelian groups, Whitehead problem and some constructions, Israel J. Math. 18 (1974), 243-256. (1974) Zbl0318.02053MR0357114
- 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. Zbl0222.02078MR0290961
- Sydow W., Über die Kategorie der topologischen Vektorräume, Doktor-Dissertation (Fernuniversität Hagen, 1980). Zbl0466.18006
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.