Let f be a real-valued function defined and continuous on the set of real numbers R. Which of the following must be true of the set S = {f(c): 0<c<1}?(adsbygoogle = window.adsbygoogle || []).push({});

I. S is a connected subset of R

II. S is an open subset of R

III. S is a bounded subset of R

The answer is I and III only. I understand why I is true. But, why is is bounded, and why is it not an open subset?

Thanks.

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# Set theory/ topology question

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