User josiah sugarman - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T02:33:40Z http://mathoverflow.net/feeds/user/2224 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/7782/are-the-inner-automorphisms-the-only-ones-that-extend-to-every-overgroup Are the inner automorphisms the only ones that extend to every overgroup? Josiah Sugarman 2009-12-04T16:22:59Z 2010-01-07T00:01:19Z <p>Let H be a group. Can we find an automorphism $\phi :H\rightarrow H$ which is not an inner automorphism, so that given any inclusion of groups $i:H\rightarrow G$ there is an automorphism $\Phi: G\rightarrow G$ that extends $\phi$, i.e. $\Phi\circ i=i\circ \phi$?</p> http://mathoverflow.net/questions/8445/learning-topology/8456#8456 Answer by Josiah Sugarman for Learning Topology Josiah Sugarman 2009-12-10T14:21:34Z 2009-12-12T08:06:49Z <p>For General Topology I recommend Kelley's book.</p> <p>I learned general topology with a book that only contained theorems and I referred to Kelley when I had too much difficulty proving them. This method of learning works very well with General topology since most of the proofs are straight forward.</p> http://mathoverflow.net/questions/3559/colloquial-catchy-statements-encoding-serious-mathematics/3618#3618 Comment by Josiah Sugarman Josiah Sugarman 2009-12-10T15:59:23Z 2009-12-10T15:59:23Z You need Banach's fixed point for the uniqueness, but the existence follows Brouwer's fixed point. http://mathoverflow.net/questions/8445/learning-topology/8452#8452 Comment by Josiah Sugarman Josiah Sugarman 2009-12-10T14:12:57Z 2009-12-10T14:12:57Z I love Hatcher's book. It's very easy to read. Honestly, I've never read it through and I only use it as a reference. http://mathoverflow.net/questions/8257/mathematical-definition-of-running Comment by Josiah Sugarman Josiah Sugarman 2009-12-09T02:20:12Z 2009-12-09T02:20:12Z @Alberto I don't like the fact that someone systematically downvoted fpqc's answers and questions. His questions and answers are generally good. Up and Down voting is important and should not be a petty vengeful act. fpqc is not nice, but all the downvoting he does is intended to make the site better. And the majority (though not VAST majority) of his downvotes, including the one toward one of my answers, appears to be correct. http://mathoverflow.net/questions/7983/does-this-inequality-hold/8000#8000 Comment by Josiah Sugarman Josiah Sugarman 2009-12-07T00:32:06Z 2009-12-07T00:32:06Z I'm gonna delete my answer before my Rep. goes down any further add simultaneously win the first peer pressure badge. http://mathoverflow.net/questions/7983/does-this-inequality-hold/7991#7991 Comment by Josiah Sugarman Josiah Sugarman 2009-12-06T13:02:50Z 2009-12-06T13:02:50Z Sorry about that, I knew it was morally wrong while I was doing it and couldn't help myself.