Characterizations of submetacompactness

We give an internal characterization of submetacompactness and then we use it to prove that a space X is submetacompact if and only if X × (κ + 1) is suborthocompact, where κ is a cardinal no less than the Lindelöf degree of X. Similarly, we also obtain that a space X is metacompact if and only if X × (κ + 1) is orthocompact.