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seen Aug 14 '10 at 15:55
I like math.

Sep
24
awarded  Autobiographer
Jul
7
awarded  Popular Question
Mar
30
awarded  Nice Question
Mar
21
awarded  Yearling
May
20
comment Why is Lebesgue integration taught using positive and negative parts of functions?
Completion of what? I understand how the extended reals can be seen as an order completion of ${\mathbb R}.$ But what does metric completion have to do with vector valued integrals? What are we metrically completing? ${\mathbb R}$ is already complete. The connection between order and monotone convergence makes sense. But the examples of the "metric" approach seem off topic. Are you saying convergence in measure and completeness of $L_p$ are more natural if you avoid the extended reals? I don't get it.
May
18
answered Why is Lebesgue integration taught using positive and negative parts of functions?
May
18
answered a.e. convergence of the powers of an operator built from rotations
May
10
comment How can one characterise compactness-by-experiment?
This was already covered in his question when he mentioned homotopy theory.
May
10
comment Examples of common false beliefs in mathematics
Remember being confused by this too. It became much clearer when I formally was taught about short exact sequences. Then you can see exactly the obstruction to such a decomposition.
May
2
comment Two commuting mappings in the disk
A related tangent: applying this other Kakutani Fixed-point theorem (en.wikipedia.org/wiki/Kakutani_fixed_point_theorem) to the multi-valued function $g^{-1} \circ f$ looks like it solves the problem... unfortunately the sets $f^{-1}( g(x))$ aren't convex (which is a pretty significant assumption!)
Apr
14
comment 2, 3, and 4 (a possible fixed point result ?)
@Ady: Since your question is whether or not $FP(2,3,4)$ holds, I'm confused. You seem to be claiming that BGK resolves your question.
Apr
6
comment 2, 3, and 4 (a possible fixed point result ?)
For fun, I started considering variants of this question but made no real progress on them either. Let ${\bf FP}(p,q,r)$ be the same statement with $2,3,4$ replaced by $p,q,r$. The BGK fixed point theorem gives us ${\bf FP}(p,p,p)$ for $1 < p < \infty.$ For what other values of $p,q,r$ can you prove or disprove this statement? Do you know of a counterexample to $FP(1,\infty, \infty)$?
Mar
30
revised Topologizing free abelian groups
added 26 characters in body
Mar
30
revised Topologizing free abelian groups
fixed the topology
Mar
30
awarded  Commentator
Mar
30
comment Topologizing free abelian groups
I've edited the uniqueness part to make it more convincing.
Mar
30
revised Topologizing free abelian groups
clarified uniqueness
Mar
30
comment Topologizing free abelian groups
Chris Schomer-Preis' comment made me think a little more. I was under the impression that my construction worked at least when $S$ was something nice like compact metric. If it goes wrong with a stranger space $S$ (as suggested by Dominguez below) then it would be really interesting to see some examples.
Mar
30
revised Topologizing free abelian groups
Added existence portion of argument
Mar
30
answered Topologizing free abelian groups