*Definition [#fa8c39f4]
n denotes a positive integer.
Let X be a topological space. Then X is called n-boundedly paracompact provided that n is the least positive integer such that if C is an open cover of X, then C has a [[locally finite]] open refinement of [[order>order (point-finiteness)]] n.

*Reference [#db212d20]
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.