Chapter 3
accumulation point of A, and the condition for f to be continuous at 0 is that lim n!1 yn = y0. As for limits, we can give an equivalent sequential definition of continuity, which follows immediately from Theorem 2.4. Theorem 3.6. If f: A → R and c ∈ A is an accumulation point of A, then f is continuous at c if and only if lim n!1 f(xn) = f(c)
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