Neighborhood basis of the identity in a locally profinite group - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T22:50:06Z http://mathoverflow.net/feeds/question/98031 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/98031/neighborhood-basis-of-the-identity-in-a-locally-profinite-group Neighborhood basis of the identity in a locally profinite group Niccolo' 2012-05-26T08:47:53Z 2012-05-26T16:47:36Z <p>Consider a locally profinite group \$G\$, i.e. a locally compact, totally disconnected topological group. Suppose it admits an open maximal compact subgroup named \$K\$. It is known that \$G\$ admits as a neighborhood basis of the identity element a collection \${ K_i }\$ of open compact subgroups, but what can we say about the countability of this family? </p> <p>In the basic examples I know, \$GL_1(\mathbb{Q}_p)\$ and \$GL_2(\mathbb{Q}_p)\$, the family \${K_i}\$ is in fact countable, is it always true? Any reference is greatly appreciated, thanks.</p> http://mathoverflow.net/questions/98031/neighborhood-basis-of-the-identity-in-a-locally-profinite-group/98052#98052 Answer by Igor Rivin for Neighborhood basis of the identity in a locally profinite group Igor Rivin 2012-05-26T16:47:36Z 2012-05-26T16:47:36Z <p>Check out <a href="http://www.math.ubc.ca/~cass/research/pdf/Profinite.pdf" rel="nofollow">Casselman's notes.</a> They are quite enlightening, and just came up yesterday for <a href="http://mathoverflow.net/questions/97971/haar-measure-for-profinite-groups-reference-needed" rel="nofollow">another question.</a></p>