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Thread: Finding a Hamel base.

  1. #1
    May 2008

    Finding a Hamel base.

    Let X be a non-empty set, and let $\displaystyle \mathcal{\mathcal{H}}$ be the set of functions $\displaystyle \mathcal{H}=\left\{ f\,:\, X\rightarrow\mathbb{C}:\, f(x)=0\text{ for all but a finite number of points } x\in X\right\}$ equipped with the usual pointwise vector operations. For each $\displaystyle f\in\mathcal{H}$, define the subset S(f) of X by $\displaystyle S(f)=\left\{ x\in X\::\: f(x)\neq0\right\}$
    Exhibit an explicit Hamel base for $\displaystyle \mathcal{H}$, showing that it satisfies all the requirements of such a base.
    Last edited by Opalg; Feb 21st 2010 at 12:40 AM. Reason: Fixed LaTeX
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