friends! Let $X$ be a topological vector space equipped with the structure of an algebra over the field $\mathbb{C}$.
Is the multiplication $X\times X\to X ,(x,y)\mapsto xy$ continuous with respect to the product topology of $X\times X$ for generical topological vector space or, at least, for normed ones? If it is, could anybody so kind to give a proof or a link to a proof?
Thank you all!!!