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

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
Re: Principal Reliods
Posted: Nov 1, 2013 9:55 PM

On Fri, 1 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.

Date Subject Author
10/25/13 Victor Porton
10/25/13 Peter Percival
10/25/13 fom
10/25/13 William Elliot
10/26/13 William Elliot
10/26/13 Victor Porton
10/26/13 William Elliot
10/27/13 Victor Porton
10/27/13 William Elliot
10/28/13 Victor Porton
10/29/13 William Elliot
10/29/13 Victor Porton
10/30/13 William Elliot
10/30/13 Victor Porton
10/30/13 William Elliot
10/31/13 Victor Porton
11/1/13 William Elliot
11/1/13 Victor Porton
11/1/13 William Elliot
11/2/13 Victor Porton
11/2/13 William Elliot
11/3/13 Victor Porton
11/3/13 Victor Porton
11/3/13 William Elliot
11/4/13 William Elliot
11/4/13 Victor Porton
11/5/13 William Elliot
11/5/13 Victor Porton
11/6/13 William Elliot
11/6/13 Victor Porton
11/6/13 William Elliot
11/7/13 Victor Porton
11/7/13 William Elliot
11/8/13 William Elliot
11/8/13 Victor Porton
11/8/13 William Elliot
11/9/13 Victor Porton
11/9/13 William Elliot
11/9/13 William Elliot
11/9/13 Victor Porton
10/26/13 Victor Porton