(α,β)-metacompact

Definition

• A topological space X is (α,β)-metacompact iff every open cover U of X of cardinality at most α has an open refinement V covering X and such that ord (x,V) < β for each x in X. (α,β are cardinal number and α≦β)

Reference

• Scott, Brian M., More about orthocompactness., Topology, Proc. Conf., Vol. 5, Birmingham/Ala. 1980, 155-184 (1981).