User ramón barral - MathOverflow

Answer by Ramón Barral for Awfully sophisticated proof for simple facts

2012-11-09T19:32:14Z

Seen on http://legauss.blogspot.com.es/2012/05/para-rir-ou-para-chorar-parte-13.html

Theorem: $5!/2$ is even.

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.

Sigma-compactness in Furstenberg paper

2012-09-23T02:28:34Z

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.

The question is: is there such a proof, or does this mean his theorems about quasi-isometric flow have a lesser degree of generality?

Non trivial vector bundle over non-paracompact contractible space

2012-09-06T11:06:24Z

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:

Non trivial vector bundles over a paracompact non-Hausdorff contractible space

Non trivial vector bundles over a Hausdorff non-paracompact contractible space

Non trivial vector bundles over a non-Hausdorff non-paracompact contractible space

Comment by Ramón Barral

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.