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order (point-finiteness)

Last-modified: 2010-08-15 (日) 15:25:46

Definition Edit

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 Edit

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.