Prove that if f is uniformly continuous on a bounded set S then f is bounded on S.(adsbygoogle = window.adsbygoogle || []).push({});

Our book says uniform continuity on an interval implies regular continuity on the interval, and in the previous chapter we proved that if a function is continuous on some closed interval then it is bounded. Is that how I should prove this, or am I missing something? It seems to easy this way and that usually means I am overlooking something.

tia

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# Uniform continuity and bounded

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