EVERY TOTALLY DISCONNECTED SEPARABLE METRIZABLE TOPOLOGICAL GROUP IS AN AUTOHOMEOMORPHISM GROUP

被引：1
作者：
VANMILL, J
机构：
[1] FREE UNIV AMSTERDAM,FAC WISKUNDE & INFORMAT,1081 HV AMSTERDAM,NETHERLANDS
[2] UNIV AMSTERDAM,FAC WISKUNDE & INFORMAT,1018 WB AMSTERDAM,NETHERLANDS
来源：
TOPOLOGY AND ITS APPLICATIONS | 1990年 / 35卷 / 2-3期
关键词：
compact open topology; Hilbert space; homeomorphism group; space of measurable functions; totally disconnected space;
D O I：
10.1016/0166-8641(90)90098-M
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
De Groot proved that every group is the autohomeomorphism group of some metrizable space. A space is totally disconnected if every connected subset of it contains at most one point. We prove that every separable metrizable totally disconnected topological group is topologically isomorphic to the autohomeomorphism group of some separable metrizable space, when given the compact-open topology. It is known that, for example, the circle group cannot be realized in this way. © 1990.
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页码：127 / 135
页数：9
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