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




Re: Product, Filters and Quantales
Posted:
Oct 15, 2013 12:05 AM


On Mon, 14 Oct 2013, Victor Porton wrote: > William Elliot 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}} = { A in P(R)  {0} subset A }? > Clearly the second. > > up {0} is the principal filter on R generated by the set {0} > > >> G_e = up{0} x (e;+oo)
Error: G_e is not a reloid for P(R) x P(R).
> >> >> Then /\G = up{0} x up(e;+oo)
> > 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}
Another error. What the hence do you mean? up{{0}} x up{ (e,oo)  0 < e } ?
If you do, then a mistake for up{ (e,oo)  0 < e } /= up{{0}}.
> >> >> So F o inf_k Gk != inf{ F o Gk  k in K }



