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Jul 20, 2015 at 2:46 comment added Kevin Casto In that case, you can just view the union of all the spaces as a subset of $\mathbb C^\infty$. Thus a sequence of rational functions converges when its coefficients converge.
Jul 19, 2015 at 13:32 history edited Joe Silverman CC BY-SA 3.0
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Jul 19, 2015 at 12:57 comment added Arnold Neumaier I need a single space independent of $d$.
Jul 19, 2015 at 11:48 history answered Joe Silverman CC BY-SA 3.0