Results 1 to 1 of 1

Thread: Finding a Hamel base.

  1. #1
    May 2008

    Finding a Hamel base.

    Let X be a non-empty set, and let \mathcal{\mathcal{H}} be the set of functions \mathcal{H}=\left\{ f\,:\, X\rightarrow\mathbb{C}:\, f(x)=0\text{ for all but a finite number of points } x\in X\right\} equipped with the usual pointwise vector operations. For each f\in\mathcal{H}, define the subset S(f) of X by S(f)=\left\{ x\in X\::\: f(x)\neq0\right\}
    Exhibit an explicit Hamel base for \mathcal{H}, showing that it satisfies all the requirements of such a base.
    Last edited by Opalg; Feb 21st 2010 at 01:40 AM. Reason: Fixed LaTeX
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Hamel basis
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Sep 30th 2011, 05:54 AM
  2. Finding unknown base from equation
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Jan 31st 2011, 10:36 PM
  3. Replies: 6
    Last Post: Jun 6th 2010, 07:00 AM
  4. Replies: 1
    Last Post: Mar 7th 2010, 07:14 PM
  5. Finding the base of an exponent
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Jan 21st 2010, 07:21 PM

Search Tags

/mathhelpforum @mathhelpforum