homeomorphism of topological group - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T01:12:51Z http://mathoverflow.net/feeds/question/74487 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/74487/homeomorphism-of-topological-group homeomorphism of topological group jasp 2011-09-04T04:05:53Z 2011-09-04T04:50:59Z <p>Let G be a topological group and a be an element of order 2 in G. Further suppose the element a does not belong to center of G. Then is it true that only homeomorphism f of G such that $f(ax)=f(x)a$ for all x in G is $f(x)=x^{-1}$.</p> http://mathoverflow.net/questions/74487/homeomorphism-of-topological-group/74494#74494 Answer by algori for homeomorphism of topological group algori 2011-09-04T04:30:07Z 2011-09-04T04:50:59Z <p>The answer is no. Take $H$ any topological group, $H'$ another topological group having a noncentral element $a'$ of order 2, $G=H\times H'$, $a=1_H\times a'$ and $f=h\times inv_{H'}$ where $h$ is any anti-automorphism of $H$ and $inv_{h'}$ is the map $h'\mapsto h'^{-1},h'\in H'$.</p>