Generalized paracompactness of subspaces in products of two ordinals

AbstractWe will characterize metacompactness, subparacompactness and paracompactness of subspaces of products of two ordinal numbers. Using them we will show: 1.For such subspaces, weak submetaLindelöfness, screenability and metacompactness are equivalent.2.Metacompact subspaces of ω12 are paracompact.3.Metacompact subspaces of ω22 are subparacompact.4.There is a metacompact subspace of (ω1+1)2 which is not paracompact.5.There is a metacompact subspace of (ω2+1)2 which is not subparacompact