*Definition [#td6b6f6f]
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 [#r15fd007]
-cf. [[submetacompact]], [[weakly κ-submetacompact]]
*Reference [#x9fcc8cf]
N. Kemoto, Y. Yajima, ''Orthocompactness in infinite product spaces'', Proc. Amer. Math. Soc. Vol.120 No.2 (1994)