Band of topological groups

In this article, we construct a band of topological groups from a cryptogroup. Also, we prove that a band of topological groups is metrizable if and only if each $\mathcal{H}$-class is metrizable. Finally, we demonstrate that if $S$ is a band of topological groups and $N$ is a full normal subcryptogroup of $S$, then $S\mathrm{/}N$ is Hausdorff if and only if ${\rho }_{{}_N}$ is closed in $S\times S$ if and, ${\rho }_{{}_N}$ is closed in $S\times S$ if and only if $N$ is closed in $S$.