Building Suitable Sets For Locally Compact Groups By Means Of Continuous Selections

Dmitri Shakhmatov

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Building Suitable Sets For Locally Compact Groups By Means Of Continuous Selections

机译：通过连续选择为局部紧凑型群体构建合适的集合

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If a discrete subset S of a topological group C with the identity 1 generates a dense subgroup of C and S ∪ (1) is closed in C, then 5 is called a suitable set for G. We apply Michael's selection theorem to offer a direct, self-contained, purely topological proof of the result of Hofmann and Morris [K.-H. Hofmann, S.A. Morris, Weight and c, J. Pure Appl. Algebra 68 (1-2) (1990) 181-194] on the existence of suitable sets in locally compact groups. Our approach uses only elementary facts from (topological) group theory.

机译：如果具有标识1的拓扑组C的离散子集S生成C的密集子组，并且S∪（1）在C中闭合，则5被称为G的合适集合。我们应用迈克尔的选择定理提供了直接，是霍夫曼和莫里斯[K.-H. Hofmann，S.A。Morris，Weight和c，J。Pure Appl。代数68（1-2）（1990）181-194]。我们的方法仅使用（拓扑）群论中的基本事实。

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《Topology and its applications》 |2009年第7期|1216-1223|共8页
作者
Dmitri Shakhmatov;
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正文语种 eng
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关键词
locally compact group; generating rank; suitable set; lower semicontinuous; set-valued map; selection; converging sequence; compactly generated;

机译：局部紧致群;生成秩;合适集;下半连续;集值映射;选择;收敛序列;紧凑生成;

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6. A Decomposition of Compact Continua and Related Theorems on Fixed Sets under Continuous Transformations [O] . J. L. Kelley 1940

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7. Building suitable sets for locally compact groups by means of continuous selections [O] . Shakhmatov Dmitri 2009

机译：通过连续选择为局部紧凑型群体构建合适的组合

Building Suitable Sets For Locally Compact Groups By Means Of Continuous Selections

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