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,