TURNING AUTOMATIC CONTINUITY AROUND: AUTOMATIC HOMOMORPHISMS

Ryan M. Berndt; Greg G. Oman

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TURNING AUTOMATIC CONTINUITY AROUND: AUTOMATIC HOMOMORPHISMS

机译：围绕自动连续性：自动同态

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Let G and H be Polish groups and let π:G → H be a function. The automatic continuity problem is the following: assuming π is a group homomorphism, find conditions on G, H, or π which imply that π is continuous. In this note, we initiate a study of a reverse problem: supposing π is continuous, find conditions on G, H, or π which imply that π is a homomorphism. Herein, we treat the case G = H = R.

机译：令G和H为波兰族，令π：G→H为一个函数。自动连续性问题如下：假设π是群同态，则在G，H或π上找到条件，这表明π是连续的。在本文中，我们开始研究一个反向问题：假设π是连续的，在G，H或π上找到条件，这意味着π是同态。在这里，我们处理G = H = R的情况。

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来源
《Real analysis exchange》 |2016年第2期|271-286|共16页
作者
Ryan M. Berndt; Greg G. Oman;
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作者单位

Department of Mathematical Sciences, Otterbein University,Westerville, OH 43081, U.S.A;

Department of Mathematics, University of Colorado,Colorado Springs, CO 80918, U.S.A;

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原文格式 PDF
正文语种 eng
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关键词
automatic continuity; homomorphism; lattice; Polish group;

机译：自动连续性;同态格子;波兰集团;

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TURNING AUTOMATIC CONTINUITY AROUND: AUTOMATIC HOMOMORPHISMS

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