boundedly metacompact

Definition

A topological space X is called boundedly metacompact provided that if Q is an open cover of X, then there is a positive integer n such that Q has a point-finite open refinement of order n.

Reference

P. Fletcher, R.A. Mccoy AND R. Slover, On Boundedly Metacompact And Boundedly Paracompact Spaces, Proc. Amer. Math. Soc, Vol. 25, No. 2 (1970), pp.335-342.