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Re: Product, Filters and Quantales
Posted:
Oct 12, 2013 11:45 PM


On Sat, 12 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) ? > Yes.
D is the neighborhood filter for 0 in 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 }?
So which is it for up 0? The first or the second? BTW, the first is a filter on (R,<=).
> G_e = up{0} x (e;+oo) > > >> Then /\G = up{0} x up(e;+oo) > Which is correct? up(e,oo) = { x in R  e < 0 } is a filter on (R,<=) or up(e,oo) = { A in P(R)  (e,oo) subset A } a filter for R on P(R)?
> G = { G_e  e>0 } > > >> up{0} x (e;+oo) = up{0} x up{0} > >> > >> So F o inf_k Gk != inf{ F o Gk  k in K }



