Here is the problem:
I'm so hopelessly lost... Help Please!!!!
A metric space is compact if and only if it's totally bounded and complete. I bet you know that $\displaystyle \mathbb{Q}$ is not totally bounded (under the usual metric), $\displaystyle \mathbb{Q}_{[0,1]}$ is not complete, $\displaystyle \mathbb{R}$ is not totally bounded
try d)
Also, consider that in a metric space (or in a more general scenario) if $\displaystyle x_n\to x$ then $\displaystyle C=\{x\}\cup\left\{x_m:m\in\mathbb{N}\right\}$ is compact. See if that helps