For a space X, 2X denotes the collection of all non-empty closed sets of X with the Vietoris topology, and K(X) denotes the collection of all non-empty compact sets of X with the subspace topology of 2X. The following are known:•2ω is not normal, where ω denotes the discrete space of countably infinite cardinality.•For every non-zero ordinal γ with the usual order topology, K(γ) is normal iff cfγ=γ whenever cfγ is uncountable. In this paper, we will prove: (1)2ω is strongly zero-dimensional.(2)K(γ) is strongly zero-dimensional, for every non-zero ordinal γ. In (2), we use the technique of elementary submodels.