Let $X$ be a metric space and let $f : X\rightarrow R$ be a continuous function. Pick out the true statements. (a) $f$ always maps Cauchy sequences into Cauchy sequences. (b) If $X$ is compact, then $f$ always maps Cauchy sequences into Cauchy sequences. (c) If $X = R^n$, then $f$ always maps Cauchy sequences into Cauchy sequences.
If $f$ is uniformly continuous then it maps a cauchy sequence to a cauchy sequence. So, a is not true and b is true. What about c?