I know that the largest vector topology on countable dimensional vector space is sequential (i.e. every sequentially closed set is closed). Does it keep for the arbitrary vector space?
In countable dimensional case I can describe structure of largest vector topology (it coincides with the largest locally convex topology), but I don't know anything about uncountable dimensional case.
(Largest vector topology on a vector space is the supremum of set of all vector topologies on it.)