5 research outputs found
Separation with restricted families of sets
Given a finite -element set , a family of subsets is said to separate if any two elements of are separated by at
least one member of . It is shown that if ,
then one can select members of that
separate . If for some , then
members of
are always sufficient to separate all pairs of elements of that are
separated by some member of . This result is generalized to
simultaneous separation in several sets. Analogous questions on separation by
families of bounded Vapnik-Chervonenkis dimension and separation of point sets
in by convex sets are also considered.Comment: 13 page