Following earlier authors in this subject, the topology induced by a modular metric is herein called a modular topology. We show that such a topology is metrizable. More precisely, we show that the uniform topology induced by the uniformity on the modular set of a modular pseudometric is metrizable. In addition, we observe that such a topology is coarser than the underlying topology of the uniformity induced by the corresponding pseudometric. Other related immediate observations are also presented. \begin{references}{99}

\bibitem{Chistyakov2} V.V. Chistyakov, \emph{Modular metric spaces, I}: Basic concepts, Nonlinear Anal. 72 (1)(2010), 1-14.

\bibitem{Chistyakov3} V.V. Chistyakov, \emph{Modular metric spaces, II}. Application to superposition operators, Nonlinear Anal. 72 (1)(2010), 15-30. \bibitem{Chistyakov-book} V.V. Chistyakov, Metric modular spaces: Theory and applications, SpringerBriefs in Mathematics, Springer, Switzerland, 2015. \bibitem{Olela-Otafudu} Z. Mushaandja and O. Olela-Otafudu, On the modular metric topology, Topology Appl. (in press).

\end{references}

Joint work with Z. Mushaandja.