n-boundedly metacompact

Definition

n denotes a positive integer.
Let X be a topological space. Then X is called n-boundedly metacompact provided that n is the least positive integer such that if C is an open cover of X, then C 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.