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Re: Product, Filters and Quantales
Posted:
Oct 12, 2013 4:57 AM


> William Elliot wrote: > > On Thu, 10 Oct 2013, Victor Porton wrote:
> 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?)
D is a filter for R on P(R) ?
> F = D x up{0} > up {0} = { r in R  0 <= r } is not a filter. Do you mean up {{0}} = { A in P(R)  {0} subset A }?
> G_e = { up{0} x (e;+oo)  e > 0 } G_e is the collection of sets . . { up{0} x (r,+oo)  r > 0 } which doesn't vary with e.
> Then /\G = up{0} x up(e;+oo)
What's G?
> up{0} x (e;+oo) = up{0} x up{0} > > So F o inf_k Gk != inf{ F o Gk  k in K } >



