Definition
A regular Hausdorff space X is said to be semi-metacompact provided that every open cover C of X has an open refinement R so that no non-empty open subset of X is a subset of infinitely many members of R.
Reference
- Hans-Peter Kunzi and Peter Fletcher, Some Questions Related to Almost 2-Fully Normal Spaces, Rocky Mountain J. Math. Vol.15 (Nov. 1985).