κ-metacompact

Definition

α denotes a cardinal.
A topological space is called α-metacompact if each open cover with cardinality less than or equal to α has a point-finite open refinement.

Reference

N. Kemoto, Y. Yajima, Orthocompactness in infinite product spaces, Proc. Amer. Math. Soc. Vol.120 No.2 (1994).