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Re: Product, Filters and Quantales
Posted:
Oct 10, 2013 8:26 AM


William Elliot wrote:
> Upon examination, it's seen that (Ft,o,subset) is an order dual > of a quantale, a unital quantale. If, on the other hand, the > order of Ft is reversed the corollary > F o inf_k Gk = inf{ F o Gk  k in K } > inf_j Fj o G = inf{ Fj o G  j in J } > becomes > F o sup_k Gk = sup{ F o Gk  k in K } > sup_j Fj o G = sup{ Fj o G  j in J } > > Thusly (Ft,o,reversed subset) is a unital quantale.
Wrong. I have already given a counterexample in an other message.
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).



