Material: daly analysis 3.5.15. Let X be a set. Suppose that fn, f, In, 9 € Fi(X) are such thatfn → f and gn → g uniformly. Prove the following statements.(a) fn + In → f + g uniformly.(b) fn9n → fg uniformly.(c) If there is a 8 > 0 such that |gn (t)| > d for every t e X and n e N,then fn/9n → f/g uniformly.

Name: Material: daly analysis 3.5.15. Let X be a set. Suppose that fn, f, In
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Description: Material: daly analysis 3.5.15. Let X be a set. Suppose that fn, f, In, 9 € Fi(X) are such thatfn → f and gn → g uniformly. Prove the following statements.(a) fn + In → f + g uniformly.(b) fn9n → fg uniformly.(c) If there is a 8 > 0 such that |gn (t)

a. Suppose, fn→f uniformlygn→g uniformly So, there exist integers N1,N2 such that fnx-fx<ε/2…

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3.5.15. Let X be a set. Suppose that fn, f, gn, 9 € F(X) are such that fn → f and gn →g uniformly. Prove the following statements. (a) fn+gn →f + g uniformly. (b) fn9n → fg uniformly. (c) If there is a 8 >0 such that 9n (t) ≥ 8 for every t X and n € N, then fn/gn → f/g uniformly.