# Subnet or subsequence in Weak Topology?

Let $A$ be a convex and weakly compact subset of a Banach space $X$, and $\{x_n\}$ is a sequence in $A$, can we say $\{x_n\}$ has a weakly convergence sub sequence in $A$ ?

• Isn't that just the definition of weak compactness? – Roberto Rastapopoulos Mar 12 '17 at 0:52
• No, notice the word "sub sequence". Weak topology is not magnetizable in general. – Red shoes Mar 12 '17 at 0:53