Banach space and closed subspace
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Let I = [a,b] be a finite interval. Show that the space C(I,R^n) of continuous functions from I into R^n is a Banach space with the uniform norm
llull = sup l u(t) l where t is in I.
(Show that this is a norm and that C(I,R^n) is complete).
See attached file. Please be very detailed when answering question.
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Solution Summary
The solution contains a proof that a space is a Banach space with given uniform norm and a proof that a space is a closed subspace.
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