Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 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 counter-example 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).

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