In topology nowadays the value of the concept of filter is generally recognized. Since I have made essential use of the concept, in the main part of the text, I am including as an appendix a brief account of the necessary theory, although no doubt it will already be familiar to many of my readers.

Definition (A.1). A filter on a given set X is a non-empty family F of non-empty subsets of X such that

1. (i) each superset of a member of F is a member of F,

2. (ii) the intersection of a finite subfamily of F is a member of F.

In a set X the most immediately obvious filters are those which consist of all supersets of a given non-empty subset. Such filters have the property that the intersection of any family of members is also a member. This is always the case for finite sets but infinite sets contain filters which do not have this property. For example the cofinite subsets of an infinite set form a filter F0 such that the intersection of all members of F0 is empty. (A cofinite subset is the complement of a finite subset).