On The Space Of Subgroups Of A Compact Group Ii

S. Fisher; P. Gartside

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On The Space Of Subgroups Of A Compact Group Ii

机译：关于紧群Ii的子群空间

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Let C be a compact group. Let S(G), C(G), N(G) be the spaces of closed subgroups,rncosets of closed subgroups, normal closed subgroups (respectively) of G, with the Vietorisrntopology.rnThen: (1) S(G) and C(G) are never connected; (2) N(C) is always totally disconnected;rn(3) C(G) is totally disconnected if and only if G is totally disconnected; and (4) S(G) isrntotally disconnected if and only if G/Z(G) is totally disconnected.rnFurther: for totally disconnected G (equivalently, profinite G) (5) S(G), C(G) and N(G) arernκ-metrisable; (6) S(G), C(G) and N(G) are Dugundji compact if G has small weight; andrn(7) consequences for field extensions are derived.

机译：令C为一个紧凑群。令S（G），C（G），N（G）为封闭子群的空间，封闭子群的n个子集，G的正常封闭子群（分别为Vietorisrntopology.rnn）：（1）S（G）和C（G）从未连接；（2）N（C）总是完全断开； rn（3）C（G）当且仅当G完全断开时才完全断开；（4）当且仅当G / Z（G）完全断开时，S（G）才完全断开。rn：对于完全断开的G（等效地，有限的G），（5）S（G），C（G）和N （G）可测量的；（6）如果G的重量较小，则S（G），C（G）和N（G）为Dugundji紧致体； andrn（7）得出了字段扩展的结果。

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《Topology and its applications》 |2009年第5期|855-861|共7页
作者
S. Fisher; P. Gartside;
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正文语种 eng
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hyperspace; topological group;

机译：超空间;拓扑群;

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On The Space Of Subgroups Of A Compact Group Ii

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