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Proof: By the previous theorem, f (K) is compact and therefore closed and bounded by the Heine-Borel Theorem. LetS=f (K) and letmbetheleast upper bound of S, which exists ...

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The following are solutions to selected exercises from Walter RudinsPrinciplesof Mathematical Analysis, Third Edition, which I compiled during the Winter of 2008 ...

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Proof: By the previous theorem, f (K) is compact and therefore closed and bounded by the Heine-Borel Theorem. LetS=f (K) and letmbetheleast upper bound of S, which exists ...

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