*Definition [#c04514ed]
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>order (point-finiteness)]] n.
*Reference [#bc84340e]
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.