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

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
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 counter-example 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 }

Date Subject Author
10/9/13 William Elliot
10/10/13 Victor Porton
10/11/13 William Elliot
10/11/13 Victor Porton
10/12/13 William Elliot
10/12/13 Victor Porton
10/12/13 William Elliot
10/14/13 Victor Porton
10/15/13 William Elliot
10/15/13 Victor Porton
10/16/13 William Elliot
10/16/13 Victor Porton
10/17/13 William Elliot
10/17/13 Victor Porton
10/17/13 William Elliot
10/18/13 Victor Porton
10/18/13 William Elliot
10/19/13 Victor Porton
10/19/13 William Elliot
10/19/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 fom
10/21/13 fom
10/21/13 William Elliot
10/21/13 fom
10/20/13 William Elliot