1. Prove the Heine-Borel Theorem (Theorem 3.35).
2. Suppose f: X ? Y maps from the...
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1. Prove the Heine-Borel Theorem (Theorem 3.35). 2. Suppose f: X ? Y maps from the metric space X to the metricspace Y, and x ? X. Prove that f is continuous at x if and only if, for any sequence{xn} in X that converges to x, f(xn) ? f(x).
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