User dan - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T05:29:38Z http://mathoverflow.net/feeds/user/7290 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/60489/how-are-vector-spaces-viewed-as-universal-algebras how are vector spaces viewed as universal algebras? Dan 2011-04-03T20:57:36Z 2011-04-03T20:57:36Z <p>Hey I have this question from Universal Algebra texts where you can see groups, rings, lattices and other structures as Universal Algebras, but I still don't have clear how vector spaces can be viewed in this way (taking into account that all the operations in an Universal Algebra are internal: i.e, from $A^n$ to $A$)</p> <p>Thanks</p> <p>Dan</p> http://mathoverflow.net/questions/60400/question-about-free-abelian-groups Question about free abelian groups Dan 2011-04-03T01:35:48Z 2011-04-03T01:35:48Z <p>Hey I am looking at some exercise but I don't have any clue of how to solve it. It says: Let G be an infinite finitely generated abelian group and let T be the set of all the elements of G of finite order. Show that G/T is a free abelian group.</p> <p>Please, any help is welcome.</p> <p>Thanks,</p> <p>Dan</p> http://mathoverflow.net/questions/30374/problem-in-banach-space Problem in Banach space Dan 2010-07-03T05:30:19Z 2010-07-03T05:37:33Z <p>Hi everybody, I've got an exercise about Banach spaces and I can't see how to solve it. It is a very simple problem and I know it might be some little detail I'm missing, and that is why I'm asking for help.</p> <p>It says:</p> <blockquote> <p>Let X be a Banach space with a monotone basis. Let $&sigma;$ be the set of all finite block bases in the unit ball of X that contain at least one vector x<sub>i</sub> of norm 1. Suppose (y'<sub>1</sub>, z'<sub>1</sub>, y'<sub>2</sub>, z'<sub>2</sub>,...,y'<sub>n</sub>, z'<sub>n</sub>) is in $&sigma;$. Prove that the norms <code>$\Vert \sum_{i=1}^n (y'_i + z'_i)\Vert$</code> and <code>$\Vert \sum_{i=1}^n (y_i' - z'_i)\Vert$</code> are both at least 1/2.</p> </blockquote> <p>Any help is welcome. </p> <p>Thanks.</p> http://mathoverflow.net/questions/60400/question-about-free-abelian-groups Comment by Dan Dan 2011-04-03T20:43:08Z 2011-04-03T20:43:08Z yes Mark, is a homework question, and this is how I obtained my Bachelor in Mathematics for sure, thanks to mathoverflow answers... I have to tell you 2 things: First, It is foolish to think that a real mathematician would rely a forum in order to obtain a grade for a homework. And second, if that would be the case, It is my problem, not yours. It is selfish to &quot;vote to close&quot; for a question about an exercise. I think that the knowledge is for sharing, and THAT IS WHAT FORUMS ARE FOR (in case you haven't realise it). It is a shame that people like you do not allow the progress of the others. http://mathoverflow.net/questions/30374/problem-in-banach-space Comment by Dan Dan 2010-07-04T02:02:28Z 2010-07-04T02:02:28Z When you say 'tail', you mean...? http://mathoverflow.net/questions/30374/problem-in-banach-space Comment by Dan Dan 2010-07-03T15:12:36Z 2010-07-03T15:12:36Z No it isn't. It is part of a series of lemmas I'm trying to stablish for proving a theorem in other way. I would appreciate the hint, thanks for your interest.