A fundamental fact is that if we are working on a closed, bounded interval[a, b], then any continuous function f [a, b] → R is automatically uniformlycontinuous.Theorem. Suppose f [a, b] → R is continuous. Then it is uniformlycontinuous.9. Find an example of an ƒ : (0, 1) → R which is continous but not uniformlycontinuous. Where exactly did we use the fact that [a, b] was a closed andbounded interval in the proof of the theorem?

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A fundamental fact is that if we are working on a closed, bounded inter [a, b], then any continuous function f : [a, b] → R is automatically uniform continuous. Theorem. Suppose f [a, b] → R is continuous. Then it is uniform continuous. 9. Find an example of an ƒ : (0, 1) → R which is continous but not uniform continuous. Where exactly did we use the fact that [a, b] was a closed a bounded interval in the proof of the theorem?