(a) Let ACS CR, and c A be a point. Suppose f: S R is continuous...
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(a) Let ACS CR, and c A be a point. Suppose f: S R is continuous at c. Prove that the restriction f is continuous at c. (b) Find an example of a function f : S R and a subset AC S such that  is continuous at some c A but f is not continuous at c. (c) Suppose SCR such that (ca, c+a) C S for some c ER and a > 0. Let f : S R be a function and A := (ca, c+a). Prove that if  is continuous at c, then f is continuous at c. (a) Let ACS CR, and c A be a point. Suppose f: S R is continuous at c. Prove that the restriction f is continuous at c. (b) Find an example of a function f : S R and a subset AC S such that  is continuous at some c A but f is not continuous at c. (c) Suppose SCR such that (ca, c+a) C S for some c ER and a > 0. Let f : S R be a function and A := (ca, c+a). Prove that if  is continuous at c, then f is continuous at c.
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a To prove that the restriction of a function f S R is continuous at c if f is continuous at c we ca... View the full answer
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