- #1
vineethbs
- 8
- 0
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]
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.
Thank you and Merry Christmas !
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.
Thank you and Merry Christmas !