Let $X$ be a subset of a Banach space $Y$. Please can you give me a definition of what "$X$ is weakly compact" means? I want one which is in terms of sequences and boundedness, as opposed to one with topology and stuff like that. Thank you.
I have searched the internet for days to avail for such a nice definition.
I did receive an answer in this thread, however the answer makes no reference to the set $Y$. Also a citation to a text would be nice.