Let [tex]F = \left\{f : [0, \infty) \rightarrow R, norm(f) = \sup_{x \in [0,\infty)} \frac{|f(x)|}{x^{2} + 1} < \infty\right\}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Is F complete , under the given norm ?

My approach was to look at the pointwise limit of an arbitrary Cauchy sequence, but I am not able to prove that it converges in the metric induced by the norm.

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# Proving Completeness of a function space

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