*Definition [#k76aadb5]
A topological space X is called submetacompact (or θ-rifinable) if for each open cover U, 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 [#zb8e0123]
-cf. [[weakly submetacompact]], [[κ-submetacompact]]
*Reference [#w16d8e93]
N. Kemoto, Y. Yajima, ''Orthocompactness in infinite product spaces'', Proc. Amer. Math. Soc. Vol.120 No.2 (1994)