Definition:Topological Dual Space

Definition
Let $K$ be a topological field.

Let $X$ be a topological vector space over $K$.

Let $X^\ast$ be the vector space of continuous linear functionals on $X$.

We say that $X^\ast$ is the topological dual space of $X$.

Also see

 * Definition:Normed Dual Space - an instantiation of this concept in the case of $X$ a normed vector space.