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Let f, g : X −→ C denote continuous functions from the open subset X of...

Let f, g : X −→ C denote continuous functions from the open subset X of C. Use the properties of limits given in section 16 to verify the following:

(a) The sum f+g is a continuous function. (b) The product fg is a continuous function.

(c) The quotient f/g is a continuous function, provided g(z) != 0 holds for all z ∈ X.

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