# Space of continuous functions

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Let C[0,1] be the space of continuous real functions where C[0,1] has the following norm

||f||_2 =( integral (from 0 to 1) |f(t)|dt)^(1/2)

Consider f_n(t) = 0

for t greater than or equal to zero and less than or equal to 1/2-1/n,

f_n(t)=1+n(t-1/2) for t great than or equal to 1/2-1/n and t less than or equal to 1/2

and f_n(t)=1 when t is greater than or equal to 1/2 and t less than or equal to 1

Is {f_n} convergent in (C[0,1].||.||)? Justify your answer

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Â© BrainMass Inc. brainmass.com December 24, 2021, 9:16 pm ad1c9bdddf>https://brainmass.com/math/integrals/inspecting-the-space-of-continuous-functions-361062