Let $C$ be a convex subset of a locally convex topological vector space.
Consider the properties:
a) $C$ is closed.
b) $C$ is weakly closed.
c) $C$ is weakly sequentially closed.
d) $C$ is sequentially closed.
Then a) $\Leftrightarrow$ b) $\Rightarrow$ c) $\Rightarrow$ d).
Does c) imply b)?
Does d) imply c)?
(In any normed vector space, d) implies a), so all notions are equivalent for convex subsets of normed vector spaces.)