For $U$ a balanced open subset of a Fréchet space $E$ and $F$ a dual-Banach space we introduce the topology $\tau _\gamma $ on the space ${\mathcal H}(U,F)$ of holomorphic functions from $U$ into $F$. This topology allows us to construct a predual for $({\mathcal H}(U,F),\tau _\delta )$ which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions.