#7Need help with parts 1 and 2 Exercise 7. Let X be a set. We denote by B(X, K) the set of functionsf : X → K such that ||f||∞ < +∞, where||f||∞ = sup|f(x)|.TEX11) Show that the set B(X, K) is a vector space for the usual addition ofK-valued functions and the usual product of a scalar in K with a K-valuedfunction.2) Show that ||-||∞ is a norm on this vector space.

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Answered: Exercise 7. Let X be a set. We denote…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 7. Let X be a set. We denote by B(X, K) the set of functions f : X → K such that ||f||∞ < +∞, where ||f||∞ = sup|f(x)|. TEX