*Definition [#v5a4ecfb]
A topological space X is called weakly submetacompact (or weakly θ-rifinable) if for each open cover U, there exists a sequence V_n of [[weak open refinements>weak refinement]] of U such that for each x in X, V_n is point-finite at x for some n.

*Remark [#i287c516]
-cf. [[submetacompact]]

*Reference [#z9e4a844]
N. Kemoto, Y. Yajima, ''Orthocompactness in infinite product spaces'', Proc. Amer. Math. Soc. Vol.120 No.2 (1994)