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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 12, 2013 11:45 PM

On Sat, 12 Oct 2013, Victor Porton 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} = { 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 }

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