order (point-finiteness)

Definition

Let X be a topological space, let n be a positive integer and let C be a subset family of X.
C is said to be point-finite of order n iff each point in X is contained at most n members in C.
Similarly, C is said to be locally finite of order n iff each point in X has a neighborhood which intersects at most n members in C.

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.