Let $X$ be a set, a topology $\tau$ on $X$ is completely regular if, and only if, $\tau$ is the topology defined by a family of maps $\{ f_{\lambda} : X \to \mathbf{R} \}$. It is not difficult to prove that in some sense $\mathbf{R}$ is minimal under this condition. The purpose of this paper is to characterize the spaces of values $Y$ that are minimal and the families of topologies on $X$ that are complete under the property of being induced by a family of maps $\{ f_{\lambda} : X \to Y \}$.