
Filters for products
Posted:
Sep 30, 2013 11:31 PM


http://www.mathematics21.org/binaries/volume1.pdf
Definition 7.1. Why is the expression "reloid" used for (F,X,Y), a filter F for XxY?
Definition 7.5. What's a principle reloids? A reloid (F,X,Y) where F is a principle filter F_AxB, generated by {AxB} for some A subset X, B subset Y.
F_AxB = up_P(XxY) {AxB}.
Theorem 7.13 There's a direct simple proof without using the equivalence relation.
Theorem 7.14
(F,X,X) o (F,X,X) = filter generated by { AoB  A,B on F } F^1 = { A^1  A in F }; (F,X,Y)^1 = (F^1,Y,X)
(F,X,Y) o (F^1,Y,X) = filter generated by { AoB^1  A,B in F }
Theorem 7.15. The reversal of the order for filters is a nusiance, requiring always to deside which is being used. Reloids, filters for XxY, are ordered by reserse subset while, but relations R subset XxY are ordered by subset? The heck with it, too tediously confusing. Theorem ignored.
Conjecture 7.16. Expleain what an atom ofa reloid is.
Theorem 7.17. The confusing notation for meeting or not meeting, which every it may be, is cause for skipping Theorem 7.17.

