I wanted to ask the following:
Suppose I have an abelian topological $G$, and $G^*$ is its dual group (all the continuous homomorphisms from $G$ to the circle group $T$). How can I show that the family of all sets $P(K,V)$, (the subbase elements of the compact open topology where $K$ ranges over all compact subsets of $G$ containing $0$ and $V$ is the symmetric $0$ open neighborhood in the circle group) is a base of open neighborhoods of $0$ for the compact-open topology on $G^*$.
Thanks in advance for all the help.