E R", since the subset {||x – a|| | a E E} of Let E C R™ be non-empty. For -empty and bounded below by 0, its infimum exists and is non-negative. We defi = inf{||x – a|| | a E E}. ve that dp : Rm → [0, 0) is continuous on Rm. -

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Q: Let A = {0, 1} with the discrete topology and let f : A → R be defined by f(0) = −1, f(1) = 1. Show…

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Q: 7. Suppose that f: R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the…

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Q: 4. Let f: R→ R be defined by f(x) = Prove that f is continuous at 0. Sx, TEQ, (-x, -x, xER\Q.

A: Definition:A function f(x) is continuous at x=a when,lim x→a– f(x)=lim x→a+ f(x)=f(a)

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Q: 6. Let f: Q R be defined by f(x) Show that f is continuous. 0, :{ 1, = if x € (-∞, √2) nQ if x €…

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Q: let f be a non-constant analytic function in a bounded hegion Gand continuous 1. Sn G. IF f(e)+o in…

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Q: Exercise 10. Show that if ACB, then ACB.

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Q: Suppose f,g: D -> R are uniformly continuous on D. Prove that f+g is uniformly continuous on D.

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