almost m-paracompact

Definition

m denotes a cardinality.
A topological space X is said to be almost m-paracompact if for every open cover U with cardinality less than or equal to m, there exists a subset family V which refines U and whose closure covers X.

Reference

M. K. Singal, Some Generalizations of Paracompactness, Proceedings of the Kanpur topological conference, 1968. Academia Publishing House of the Czechoslovak Academy of Sciences, Praha, 1971. pp. 245-263.