Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Product, Filters and Quantales
Posted:
Oct 12, 2013 10:49 AM


William Elliot wrote:
>> 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) ?
Yes.
>> 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.
My error. Should be:
G_e = up{0} x (e;+oo)
>> Then /\G = up{0} x up(e;+oo) > > What's G?
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 }



