most recent 30 from http://mathoverflow.net 2013-05-24T16:46:18Z http://mathoverflow.net/feeds/question/107876 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107876/sigma-compactness-in-furstenberg-paper Ramón Barral 2012-09-23T02:28:34Z 2012-09-23T02:28:34Z

<p>I've been reading the classical Furstenberg paper "The structure of distal flows", where the author claims he is working with an arbitrary locally compact group $T$. Nevertheless, the proof of Lemma $5.1$ actually requires that $T$ is $\sigma$-compact. I am not aware of any proof about locally compact groups acting distally on compact metric spaces being $\sigma$-compact.</p> <p>The question is: is there such a proof, or does this mean his theorems about quasi-isometric flow have a lesser degree of generality?</p>