On comeager sets of metrics whose ranges are disconnected

For a metrizable space $X$, we denote by $\mathrm{Met}(X)$ the of all metric that generate same topology $X$. The is equipped with supremum distance. In this paper, for every strongly zero-dimensional prove set metrics whose ranges are closed totally disconnected subsets line dense $G_{\delta}$ subspace in $\mathrm{Met}(X)$. As its application, show some sets universal meager spaces metrics.