Hey,

I just moved from euclidean spaces to generic metric spaces, and I'm trying to avoid missing some basic concepts that links these spaces.

For example, in a metric space

, how can I define that some set is bounded? Can I say that

is bounded if

s.t.

? Assuming that S doesn't necessarily has a zero.

What I wanna show is that if

is compact, then every sequence in K has at least one convergent subsequence.

I can prove it in Rn using bolzano-weierstrass, but i'm unsure about what I can use in such a generic metric space.

Thanks in advance,

JP