Assume that $f: A\rightarrow W$ is sequence-compact (not sure if that is the right translation) and continuous, and $f^{-1} = g$ is not continuous but is sequence-compact, show that there is a sequence in which b in f(A) that $\lim_{n\rightarrow \infty} b_n = b $ and $\forall \epsilon>0:d(g(b_n),g(b)) > \epsilon $. (I also know that f' is also supposed to be continuous but this is for a proof by contradiction)
I know that there is a $b \in f(A)$ so that $\lim_{y\rightarrow \infty} g(y) \ne g(b)$ because g isn't continuous and that every row in f(A) is convergent to an element b in f(A) however i do not know how to show that b is the same element in both parts.