A band of topological groups is metrizable exactly when each of its H-classes is metrizable, and its quotient by a full normal subcryptogroup is Hausdorff exactly when the subcryptogroup is closed.
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Band of topological groups
A band of topological groups is metrizable exactly when each of its H-classes is metrizable, and its quotient by a full normal subcryptogroup is Hausdorff exactly when the subcryptogroup is closed.