- Please Help Solve And Explain Both Parts 1 (23.58 KiB) Viewed 34 times
please help solve and explain both parts
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answerhappygod
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please help solve and explain both parts
please help solve and explain both parts
Let bER and BCR. We call B a neighbourhood of b is there exists > 0 such that (b-e,b+e) C B. (a) Let ACR and suppose that f: A → R is continuous at E A. Prove that if B is a neighbourhood of f(x) then there exists a neighbourhood C of a such that f(Cn A) C B. (b) Let A CR, g: A → R, and a € A. Suppose that for every neighbourhood of V of g(x) there exists a neighbourhood U of a such that g(Un A) CV. Prove that g is continuous at r.
Let bER and BCR. We call B a neighbourhood of b is there exists > 0 such that (b-e,b+e) C B. (a) Let ACR and suppose that f: A → R is continuous at E A. Prove that if B is a neighbourhood of f(x) then there exists a neighbourhood C of a such that f(Cn A) C B. (b) Let A CR, g: A → R, and a € A. Suppose that for every neighbourhood of V of g(x) there exists a neighbourhood U of a such that g(Un A) CV. Prove that g is continuous at r.
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