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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

2 votes
0 answers
68 views

Topologies with the same convex closed sets

Let $\tau_1$ and $\tau_2$ be locally convex Hausdorff topologies on vector space $X$ such that $(X,\tau_1)^\ast = (X,\tau_2)^\ast$. It is well known that $(X,\tau_1)$ and $(X,\tau_2)$ have the same co …
red_alert's user avatar
  • 105
4 votes
0 answers
493 views

Every convex sequentially closed set is closed

Let $X$ be a vector space. A vector (not necessarily Hausdorff) topology on $X$ will be called convex sequential if every convex sequentially closed subset of $X$ is closed. Is there some description …
red_alert's user avatar
  • 105
4 votes
1 answer
210 views

Sequentiality of largest vector topology

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 d …
red_alert's user avatar
  • 105