κ-submetacompact

Definition

κ denotes a cardinality.
A topological space X is called submetacompact if for each open cover U with cardinality less than or equal to κ, there exists a sequence V_n of open refinements of U such that for each x in X, V_n is point-finite at x for some n.

Remark

• cf. submetacompact, weakly κ-submetacompact

Reference

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