On properties of infimal topology of a map space

We study properties of the infimal topology $\tau_\mathrm{inf}$ which is the infimum of the family of all topologies of uniform convergence defined on the set $C(X,Y)$ of continuous maps into a metrizable space $Y$. One of the main results of the research consists in obtaining necessary and sufficient condition for the topology $\tau_\mathrm{inf}$ to have the Fréchet–Urysohn property. We also establish necessary and sufficient conditions for coincidence of the topology $\tau_\mathrm{inf}$ and a topology of uniform convergence $\tau_\mu$.