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Topic: Principal Filter
Replies: 8   Last Post: Dec 7, 2013 8:31 PM

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
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 }?

Date Subject Author
11/24/13 William Elliot
11/24/13 Victor Porton
11/25/13 William Elliot
11/25/13 Roland Franzius
11/25/13 William Elliot
12/5/13 Shmuel (Seymour J.) Metz
12/7/13 William Elliot
12/7/13 Mike Terry
12/7/13 Shmuel (Seymour J.) Metz