12.7.1 Theorem
Let f:N → be a linear functional. Then:
(1) f is continuous if and only if it is bounded.
(2) f is continuous on N if and only if it is continuous at o EN.
For any linear functional f:N → F, the kernel or null space
Ker f off is defined by:
Ker f = {x E N:f(x) = 0}
and is a subspace of N.
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