weakly (m,n)-paracompact

Definition

m and n denote cardinalities.
X is said to be weakly (m, n)-paracompact if for each open covering U of X with cardinality no more than m, there exists a locally-n family V of open subsets of X which refines U and the closure of members in V cover 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.