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Topic: Product, Filters and Quantales
Replies: 31   Last Post: Oct 21, 2013 7:52 AM

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 William Elliot Posts: 2,634 Registered: 1/8/12
Product, Filters and Quantales
Posted: Oct 16, 2013 4:11 AM

On Tue, 15 Oct 2013, Victor Porton wrote:

If C subset P(S), then F(A) is the filter for S on P(S) generated by C.
If A subset S, then F_A = F{{A}) the principal filter generated by A
If F,G are filters, then F xx G = F({ AxB | A in F, B in G }).

To recap from your errors and hard to use notation, is this the counter
example for
. . F o inf_k Gk = inf{ F o Gk | k in K }
where F and the Gk's are filters for products?

D = F({ (-r,r) subset R | 0 < r }, the neighborhood filter for 0 in R.
F = D xx F_{0} is a filter for RxR on P(RxR).

> Correction:
> G_e = up{0} x up(e;+oo) where "x" means reloidal product.

Does G_r = D xx F_{(r,oo)}?

. . F o /\{ G_r | 0 < r } /= /\{ F o G_r | 0 < r }

PS. Don't forget for filters that
. . F o inf{ G_r | 0 < r } = F o /\{ G_r | 0 < r }
and
. . inf{ F o G_r | 0 < r } = /\{ F o G_r | 0 < r }
where /\ is great intersection.

Date Subject Author
10/9/13 William Elliot
10/10/13 Victor Porton
10/11/13 William Elliot
10/11/13 Victor Porton
10/12/13 William Elliot
10/12/13 Victor Porton
10/12/13 William Elliot
10/14/13 Victor Porton
10/15/13 William Elliot
10/15/13 Victor Porton
10/16/13 William Elliot
10/16/13 Victor Porton
10/17/13 William Elliot
10/17/13 Victor Porton
10/17/13 William Elliot
10/18/13 Victor Porton
10/18/13 William Elliot
10/19/13 Victor Porton
10/19/13 William Elliot
10/19/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 fom
10/21/13 fom
10/21/13 William Elliot
10/21/13 fom
10/20/13 William Elliot