Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » sci.math.* » sci.math

Topic: Which term to choose?
Replies: 41   Last Post: Nov 9, 2013 5:20 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Victor Porton

Posts: 544
Registered: 8/1/05
Re: Principal Reliods
Posted: Nov 3, 2013 10:50 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

William Elliot wrote:

> On Sat, 2 Nov 2013, Victor Porton wrote:
>> William Elliot wrote:
>
>> >> > F_r = F((-r,r)) is a principal filter for R.
>> >> >
>> >> > The filter
>> >> > . . /\_(0<r) F_r = { (a,b) | a < 0 < b } }
>> >> > is not principal.

>> >>
>> >> Right.
>> >>

>> >> > Casing this into reloids,
>> >> > . . /\_(0<r) ({R} xx F_r) = {R} /\ /\_(0<r) F_r

>> >
>> >> > is the infinum of principal reloids that's not a principal reloid.
>> >
>> >> Yes, but if we limit our consideration to principal filters **only**,
>> >> then by definition any suprema and infima would be also principal.

>> > So you require that only infinums that are principal reloids to be
>> > accepted? That is not wise for, as shown above, principal reloids would
>> > not be closed under infinite infinums. Thus principal reloids aren't a
>> > complete lattice.

>>
>> You wanted to make a quantale out of principal reloids. To make it one
>> need to restrict suprema and infima only to principal reloids. The
>> resulting quantale is isomorphic to the quantale of binary relation, so
>> it is effectively nothing new.
>>

> It's not possible because infinite infinums of principal reloids
> isn't a pricipal reloid. In addition, for closure of compositions
> the reloids cannot be a filter on a product of different sets;
> they need to be a filter on the product of the same set.


Suprema and infima depends on the poset on which they are taken.

If we take suprema and infima on the poset of principal reloids, then the
suprema and infima are by definition principal reloids.

This is obviously a quantale bijective to the quantale of binary relations.

>> Topic closed.
>
> There is an isomophism but it not a complete isomorphism.
>
> Topic over.


Well, there are nothing interesting about this.


Date Subject Author
10/25/13
Read Which term to choose?
Victor Porton
10/25/13
Read Re: Which term to choose?
Peter Percival
10/25/13
Read Re: Which term to choose?
fom
10/25/13
Read Re: Which term to choose?
William Elliot
10/26/13
Read Re: Which term to choose?
William Elliot
10/26/13
Read Re: Which term to choose?
Victor Porton
10/26/13
Read Re: Which term to choose?
William Elliot
10/27/13
Read Re: Which term to choose?
Victor Porton
10/27/13
Read Re: Which term to choose?
William Elliot
10/28/13
Read Re: Which term to choose?
Victor Porton
10/29/13
Read Re: Which term to choose?
William Elliot
10/29/13
Read Re: Which term to choose?
Victor Porton
10/30/13
Read Principal Reliods
William Elliot
10/30/13
Read Re: Principal Reliods
Victor Porton
10/30/13
Read Re: Principal Reliods
William Elliot
10/31/13
Read Re: Principal Reliods
Victor Porton
11/1/13
Read Re: Principal Reliods
William Elliot
11/1/13
Read Re: Principal Reliods
Victor Porton
11/1/13
Read Re: Principal Reliods
William Elliot
11/2/13
Read Re: Principal Reliods
Victor Porton
11/2/13
Read Re: Principal Reliods
William Elliot
11/3/13
Read Re: Principal Reliods
Victor Porton
11/3/13
Read Re: Principal Reliods
Victor Porton
11/3/13
Read Re: Principal Reliods
William Elliot
11/4/13
Read Principal Reliods
William Elliot
11/4/13
Read Re: Principal Reliods
Victor Porton
11/5/13
Read Re: Principal Reliods
William Elliot
11/5/13
Read Re: Principal Reliods
Victor Porton
11/6/13
Read Partition of a filter
William Elliot
11/6/13
Read Re: Partition of a filter
Victor Porton
11/6/13
Read Re: Partition of a filter
William Elliot
11/7/13
Read Re: Partition of a filter
Victor Porton
11/7/13
Read Re: Partition of a filter
William Elliot
11/8/13
Read Partition of a filter
William Elliot
11/8/13
Read Re: Partition of a filter
Victor Porton
11/8/13
Read Re: Partition of a filter
William Elliot
11/9/13
Read Re: Partition of a filter
Victor Porton
11/9/13
Read Re: Partition of a filter
William Elliot
11/9/13
Read Re: Partition of a filter
William Elliot
11/9/13
Read Re: Partition of a filter
Victor Porton
10/26/13
Read Re: Which term to choose?
Victor Porton
11/4/13
Read Re: Which term to choose?
aliahmadikram

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.