• van Dantzig’s theorem

    Updated: 2011-05-31 01:35:51
    This is yet another post in a series on basic ingredients in the structural theory of locally compact groups, which is closely related to Hilbert’s fifth problem. In order to understand the structure of a topological group , a basic strategy is to try to split into two smaller factor groups by exhibiting a short [...]

  • Doc Savage | Bad Astronomy

    Updated: 2011-05-29 14:30:54
    Subscribe Give a Gift Archives Customer Service SEARCH Health Medicine Mind Brain Technology Space Human Origins Living World Environment Physics Math Video Photos Podcast RSS Look hoo’s back 3rd Annual 3QuarksDaily science writing contest open Doc Savage Two of my favorite things in the world are Doctor Who and My Close Personal Friend Adam Savage So what could be better than a video combining them , and throwing in two giant Tesla coils and a Faraday cage I think I have nothing to add to . this May 29th , 2011 7:30 AM Tags : Adam Savage ArcAttack Doctor Who Faraday cage Tesla coils by Phil Plait in Cool stuff Geekery Humor SciFi TV Movies 26 comments RSS feed Trackback 26 Responses to Doc Savage” 1. Zucchi Says : May 29th , 2011 at 7:37 am I’ve been hoping Adam would earn a PhD so I

  • The Symmetry of Sleep | The Loom

    Updated: 2011-05-28 19:57:33
    Subscribe Give a Gift Archives Customer Service SEARCH Health Medicine Mind Brain Technology Space Human Origins Living World Environment Physics Math Video Photos Podcast RSS Arsenic life redux : how arseniclife helped change science Lisa Randall to judge this year’s 3 Quarks Daily science prize . Send in your nomination The Symmetry of Sleep The World Science Festival is going to kick off on Wednesday in New York I’ll be speaking Thursday on a panel , on telling the stories of science in print and online . The festival organizers have been publishing a blog on some of the topics that will be explored next week . Riffing on the session on sleep I’ve just contributed a piece on some wonderful recent research on what it means for us to be asleep and to be awake–and the surprising porous

  • Locally compact groups with faithful finite-dimensional representations

    Updated: 2011-05-27 21:32:19
    This is another post in a series on various components to the solution of Hilbert’s fifth problem. One interpretation of this problem is to ask for a purely topological classification of the topological groups which are isomorphic to Lie groups. (Here we require Lie groups to be finite-dimensional, but allow them to be disconnected.) There [...]

  • Locally compact topological vector spaces

    Updated: 2011-05-24 19:06:45
    Recall that a (real) topological vector space is a real vector space equipped with a topology that makes the vector space operations and continuous. One often restricts attention to Hausdorff topological spaces; in practice, this is not a severe restriction because it turns out that any topological vector space can be made Hausdorff by quotienting [...]

  • In Calculus too 1 = 0

    Updated: 2011-05-22 23:59:03
    In Calculus too 1 = 0

  • The Birkhoff-Kakutani theorem

    Updated: 2011-05-18 00:29:03
    A topological space is said to be metrisable if one can find a metric on it whose open balls generate the topology. There are some obvious necessary conditions on the space in order for it to be metrisable. For instance, it must be Hausdorff, since all metric spaces are Hausdorff. It must also be first [...]

  • Ado’s theorem

    Updated: 2011-05-11 00:00:06
    Recall that a (complex) abstract Lie algebra is a complex vector space (either finite or infinite dimensional) equipped with a bilinear antisymmetric form that obeys the Jacobi identity (One can of course define Lie algebras over other fields than the complex numbers , but in order to avoid some technical issues we shall work solely [...]

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