A REFLEXIVE ADMISSIBLE TOPOLOGICAL GROUP MUST BE LOCALLY COMPACT

被引：13
作者：
MARTINPEINADOR, E
机构：
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 123卷 / 11期
关键词：
ADMISSIBLE TOPOLOGY; COMPACT OPEN TOPOLOGY; REFLEXIVE GROUP; CONTINUOUS CONVERGENCE STRUCTURE; LOCALLY COMPACT;
D O I：
10.2307/2161108
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a reflexive topological group, and G(boolean AND) its group of characters, endowed with the compact open topology. We prove that the evaluation mapping from G(boolean AND) x G into the torus T is continuous if and only if G is locally compact. This is an analogue of a well-known theorem of Arens on admissible topologies on C(X).
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收藏
页码：3563 / 3566
页数：4
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[42]   Forcing with a coherent Souslin tree and locally countable subspaces of countably tight compact spaces [J].
Fischer, A. J. ;
Tall, F. D. ;
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[44]   C*-algebras, H*-algebras and trace ideals of pseudo-differential operators on locally compact, Hausdorff and abelian groups [J].
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[45]   Applications of some strong set-theoretic axioms to locally compact T5 and hereditarily scwH spaces [J].
Nyikos, PJ .
FUNDAMENTA MATHEMATICAE, 2003, 176 (01) :25-45
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