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

 Messages: [ Previous | Next ]
 Victor Porton Posts: 621 Registered: 8/1/05
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 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.

>> 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 }

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