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Re: Product, Filters and Quantales
Posted:
Oct 11, 2013 7:56 AM


William Elliot wrote:
> On Thu, 10 Oct 2013, Victor Porton wrote: > >> > F o inf_k Gk = inf{ F o Gk  k in K } >> > inf_j Fj o G = inf{ Fj o G  j in J } >> >> Wrong. I have already given a counterexample in an other message. > > I disagreed with the counter example and didn't keep it. > In this notation (subset order), what is the counter example.
What do you mean by "disagreed"?
The following is a counterexample for
F o inf_k Gk = inf{ F o Gk  k in K }
Let D = Ft { (e;e)  e>0 }
("Ft" means the filter generated by the given base, right?)
F = D x up{0}
G_e = { up{0} x (e;+oo)  e > 0 }
Then /\G = up{0} x up(e;+oo) up{0} x (e;+oo) = up{0} x up{0}
So F o inf_k Gk != inf{ F o Gk  k in K }
>> The formula >> >> F o inf_k Gk = inf{ F o Gk  k in K } >> >> is true however when F is a principal filter. (See chapter 9 in my book). > > I'm currently at chapter 7.
I have added a new chapter 9 "On distributivity of composition with a principal reloid" to my book.



