12. Suppose that a, b E R and a < b. Show that the vector space C[a, b] of all continuous complex valued functions defined on [a, b], with supremum norm is a Banach space. ||f||= sup f(t)\, te [a,b]

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Q: (1-nt if 0 <t<n=1, if n-1<t<1. fn(t) =

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Q: 1. Let V = C[-2, 2], the vector space of continuous functions on the closed interval [-2, 2). Let f,…

A: We can just multiply h and k and integrate  Then after simplifying we are getting answer

Q: 12. Suppose that a, b e R and a < b. Show that the vector space C[a, b] of all continuous complex…

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Q: Q4) Consider the space (X.Tu) and let A = [0,2) U (3) U (4,7). Find d(A), A, Aº, ext(A) and b(A).

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Q: Show how a real

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Q: sup norm

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Q: 4) Let ƒz = dƒ/əz and ƒz = 0ƒ/əz. Recall ƒ = u + iv, the notation f is used for the complex…

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