1. Prove the Heine-Borel Theorem (Theorem 3.35). 2. Suppose f: X → Y maps from the...

1. Prove the Heine-Borel Theorem (Theorem 3.35).
2. Suppose f: X → Y maps from the metric space X to the metric space 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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Colby Messinger answered 5 months ago

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