User arun s - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T15:40:22Z http://mathoverflow.net/feeds/user/996 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/25630/major-mathematical-advances-past-age-fifty/25635#25635 Answer by arun s for Major mathematical advances past age fifty arun s 2010-05-23T07:32:13Z 2010-05-23T07:32:13Z <p>Weierstrass approximation theorem was proved by Karl Weierstrass when he was 70 years old</p> http://mathoverflow.net/questions/25578/limiting-behaviour-of-converging-loops-on-a-torus limiting behaviour of converging loops on a torus arun s 2010-05-22T12:09:05Z 2010-05-22T20:17:16Z <p>Suppose (L<sub>n</sub>) is a sequence of loops in a torus S<sup>1</sup> &times; S<sup>1</sup> converging in the Hausdorff metric to some set L in the torus. Suppose also that for each loop L<sub>n</sub> the projection map p:S<sup>1</sup> &times; S<sup>1</sup> -> S<sup>1</sup> defined by p(x,y) =x when restricted to L<sub>n</sub> is not null-homotopic, then can we conclude that the restriction of the projection map p to L is also not null homotopic? Or are there counter examples?</p> http://mathoverflow.net/questions/4086/does-every-finitely-generated-group-have-a-maximal-normal-subgroup Does every finitely generated group have a maximal normal subgroup? arun s 2009-11-04T14:16:16Z 2010-05-17T00:42:02Z <p>Given an infinite group which is finitely generated, is there a proper maximal normal subgroup?</p> http://mathoverflow.net/questions/17388/existence-of-a-connected-set-with-given-connected-projections existence of a connected set with given connected projections. arun s 2010-03-07T16:14:04Z 2010-03-10T16:30:21Z <p>Suppose A and B are compact connected sets in the XY plane and XZ plane respectively in R^3. Suppose further that the the range of x-values taken by A and B are the same (i.e, projections of A and B onto the x-axis are the same closed interval). Is there always a connected set in R^3 whose projections onto XY and XZ planes are A and B respectively?</p> http://mathoverflow.net/questions/1894/is-amalgamation-of-groups-associative is amalgamation of groups associative arun s 2009-10-22T17:22:44Z 2009-10-22T17:29:07Z <p>Given groups $G_1, G_2, G_3$ and injections $A_1 \to G_1$ and $A_1 \to G_2$ , from $A_2 \to G_2$ and $A_2 \to G_3$, let $G_1 *_{A_1} *G_2 *_{A_2} G_3$ be the amalgam formed these groups and maps. Then is it true that $G_1 *_{A_1} *G_2 *_{A_2} G_3$ is the same as (G_1 *_{A_1} G_2 ) *_{A_2} G_3. If yes, how do we see this?</p> http://mathoverflow.net/questions/25578/limiting-behaviour-of-converging-loops-on-a-torus/25589#25589 Comment by arun s arun s 2010-05-22T17:02:02Z 2010-05-22T17:02:02Z Thanks for the answer. It appears that the notation L&lt;sub&gt;n&lt;/sub&gt; is being used in two different contexts. could you please clarify. http://mathoverflow.net/questions/17388/existence-of-a-connected-set-with-given-connected-projections/17405#17405 Comment by arun s arun s 2010-03-08T07:53:23Z 2010-03-08T07:53:23Z Nice answer!. Could you point me to a reference to the fact: &quot;a connected set in the plane can be approximated by path connected set&quot;. http://mathoverflow.net/questions/4086/does-every-finitely-generated-group-have-a-maximal-normal-subgroup/4091#4091 Comment by arun s arun s 2009-11-04T14:53:50Z 2009-11-04T14:53:50Z thank you anyway... http://mathoverflow.net/questions/4086/does-every-finitely-generated-group-have-a-maximal-normal-subgroup Comment by arun s arun s 2009-11-04T14:38:37Z 2009-11-04T14:38:37Z Yes, Iam interested in lesser goal : does one exists.