
Principal Filter
Posted:
Nov 24, 2013 3:59 AM


For not empty A subset S, let F_A be the principal filter for S generated by {A}. For x in S, let F_x = F_{x} be the principal ultrafilter for S generated by {{x}}.
Theorem. If F is a filter, then F = /\{ G ultrafilter  F subset G } Proposition. If A not empty, then F_A = /\{ F_x  x in A }.
Question. If A not empty and F a filter with F_A subset F, does F = /\{ F_x  x in A, F subset F_x }?

