Here is the problem:

http://i10.photobucket.com/albums/a1...s11787/335.jpg

I'm so hopelessly lost... Help Please!!!!

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- Mar 7th 2010, 07:18 PMPhyxius117Real analysis: Compact Sets
Here is the problem:

http://i10.photobucket.com/albums/a1...s11787/335.jpg

I'm so hopelessly lost... Help Please!!!! - Mar 7th 2010, 07:27 PMDrexel28
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