User ram&#243;n barral - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T07:37:24Z http://mathoverflow.net/feeds/user/26252 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts/111930#111930 Answer by Ramón Barral for Awfully sophisticated proof for simple facts Ramón Barral 2012-11-09T19:32:14Z 2012-11-09T19:32:14Z <p>Seen on <a href="http://legauss.blogspot.com.es/2012/05/para-rir-ou-para-chorar-parte-13.html" rel="nofollow">http://legauss.blogspot.com.es/2012/05/para-rir-ou-para-chorar-parte-13.html</a></p> <p>Theorem: $5!/2$ is even.</p> <p>Proof: $5!/2$ is the order of the group $A_5$. It is known that $A_5$ is a non-abelian simple group. Therefore $A_5$ is not solvable. But the Feit-Thompson Theorem asserts that every finite group with odd cardinal is solvable, so $5!/2$ must be an even number.</p> http://mathoverflow.net/questions/107876/sigma-compactness-in-furstenberg-paper 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> http://mathoverflow.net/questions/106497/non-trivial-vector-bundle-over-non-paracompact-contractible-space Non trivial vector bundle over non-paracompact contractible space Ramón Barral 2012-09-06T11:06:24Z 2012-09-07T15:09:14Z <p>The proof that the set of classes of vector bundles is homotopy invariant relies on the paracompactness and the Hausdorff property of the base space. Are there any known examples of:</p> <p>Non trivial vector bundles over a paracompact non-Hausdorff contractible space</p> <p>Non trivial vector bundles over a Hausdorff non-paracompact contractible space</p> <p>Non trivial vector bundles over a non-Hausdorff non-paracompact contractible space</p> http://mathoverflow.net/questions/106497/non-trivial-vector-bundle-over-non-paracompact-contractible-space/106563#106563 Comment by Ramón Barral Ramón Barral 2012-09-07T13:15:56Z 2012-09-07T13:15:56Z Thanks for your answer. This also deals with the non-paracompact non-Hausdorff case, using a suitable wedge sum with the trivial bundle over a non-paracompact contractible space, so only the Hausdorff non-paracompact case remains without an example.