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

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Victor Porton

Posts: 542
Registered: 8/1/05
Re: Product, Filters and Quantales
Posted: Oct 10, 2013 8:26 AM
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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
Read Product, Filters and Quantales
William Elliot
10/10/13
Read Re: Product, Filters and Quantales
Victor Porton
10/11/13
Read Re: Product, Filters and Quantales
William Elliot
10/11/13
Read Re: Product, Filters and Quantales
Victor Porton
10/12/13
Read Re: Product, Filters and Quantales
William Elliot
10/12/13
Read Re: Product, Filters and Quantales
Victor Porton
10/12/13
Read Re: Product, Filters and Quantales
William Elliot
10/14/13
Read Re: Product, Filters and Quantales
Victor Porton
10/15/13
Read Re: Product, Filters and Quantales
William Elliot
10/15/13
Read Re: Product, Filters and Quantales
Victor Porton
10/16/13
Read Product, Filters and Quantales
William Elliot
10/16/13
Read Re: Product, Filters and Quantales
Victor Porton
10/17/13
Read Re: Product, Filters and Quantales
William Elliot
10/17/13
Read Re: Product, Filters and Quantales
Victor Porton
10/17/13
Read Re: Product, Filters and Quantales
William Elliot
10/18/13
Read Re: Product, Filters and Quantales
Victor Porton
10/18/13
Read Re: Product, Filters and Quantales
William Elliot
10/19/13
Read Re: Product, Filters and Quantales
Victor Porton
10/19/13
Read Re: Product, Filters and Quantales
William Elliot
10/19/13
Read Mistake
William Elliot
10/20/13
Read Re: Mistake
fom
10/20/13
Read Re: Mistake
William Elliot
10/20/13
Read Re: Mistake
fom
10/20/13
Read Re: Mistake
William Elliot
10/20/13
Read Prime Interger Topology
William Elliot
10/20/13
Read Re: Prime Interger Topology
fom
10/20/13
Read Re: Prime Interger Topology
William Elliot
10/20/13
Read Re: Prime Interger Topology
fom
10/21/13
Read Re: Prime Interger Topology
fom
10/21/13
Read Re: Prime Interger Topology
William Elliot
10/21/13
Read Re: Prime Interger Topology
fom
10/20/13
Read Re: Product, Filters and Quantales
William Elliot

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