*Definition [#zf7635f8]
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>order (point-finiteness)]] n.

*Reference [#x2b8f399]
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.