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Topology

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Moderate

Relative compactness in $l^2$.

TOPO-E5LPAE

Which of the following subsets of $l^2=\{(x_1,x_2,\dots):\sum_n x_n^2<\infty\}$ is relatively compact?

A

$\{x:||x||_{l^2}=1\}$.

B

$\{x:||x||_{l^2}<1\}$.

C

$\{0\}$.

D

$\{x=(x_1,x_2,\dots x_n,\dots):|x_n|<1/n\}$.