Let $E$ be a not normable locally convex space, define $F: E'\times E\to \mathbb R$ $(f,e)\to f(e)$ I have to show that $F$ is not continuous when $E'\times E$ is given product topology.
I was reading an article and i came across with this fact.. Please give me atleast a hint to start..
My try: I know that $E$ is normable if and only if origin has a convex bounded neighborhood. So i was trying to produce any such neighborhood to contradict to assumption. Assume $F$ is continuous, then we have $\{(f,e): a
Now let $V:=\{e\in E: a
Thanks for your time.