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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 11, 2013 7:56 AM

William Elliot wrote:

> On Thu, 10 Oct 2013, Victor Porton wrote:
>

>> > F o inf_k Gk = inf{ F o Gk | k in K }
>> > inf_j Fj o G = inf{ Fj o G | j in J }

>>
>> Wrong. I have already given a counter-example in an other message.

>
> I disagreed with the counter example and didn't keep it.
> In this notation (subset order), what is the counter example.

What do you mean by "disagreed"?

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?)

F = D x up{0}

G_e = { up{0} x (e;+oo) | e > 0 }

Then /\G = up{0} x up(e;+oo)
up{0} x (e;+oo) = up{0} x up{0}

So F o inf_k Gk != inf{ F o Gk | k in K }

>> 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).

>
> I'm currently at chapter 7.

I have added a new chapter 9 "On distributivity of composition with a
principal reloid" to my book.

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