
Re: Principal Reliods
Posted:
Nov 4, 2013 5:55 AM


William Elliot wrote:
> F_A = pricnipal filter for S generated by {A} (A subset S). > F(C) = the filter for S generated by C subset P(S). > > Theorem. If for all j in J, Aj subset S, then /\_j F_Aj = F_(\/_j Aj), > The interseciton of principal filters is a principal filter. > > Do you already have a proof for that theorem? > It's a one, or at most, two line proof.
In my book:
Corollary 4.86. \uparrow is an order embedding from Z to P.
(Here Z is a set and P is the corresponding set of principal filter.)

