Dyadic mappings and dyadic superparacompact topological groups

We introduce the notion of a dyadic superparacompactum which generalizes the classical notion of a dyadic bicompactum and give an analog of V. I. Kuz'minov and L. N. Ivanovskii's Theorem on dyadicity of the space of a bicompact topological group for superparacompact groups. Moreover, we generalize L. S. Pontryagin's Theorem on existence of an open bicompact subgroup in each neighborhood of unity of a locally bicompact totally disconnected topological group.