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.independent

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 ]
William Elliot

Posts: 1,522
Registered: 1/8/12
Re: Partition of a filter
Posted: Nov 8, 2013 9:41 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Fri, 8 Nov 2013, Victor Porton wrote:
> > Are these correct?
> >
> > Definition 3.60.
> > A thorning of a point a in a complete lattice L
> > is a subset A, of L\bottom with sup S = a and
> > for all x,y in A, some d in L\bottom with d <= x,y

>
> What is "L\bottom with sup S"?
>

A thorning of a point a in a complete lattice L
is some A subset L\bottom for which sup A = a
and for all x,y in A, bottom /= x inf y.
(bottom is minimum element of L; S\a used for S\{a})

{a} is a thorning of a.

> > Definition 3.61.
> > A weak partition of an element a in a complete lattice L
> > is a subset A, of L\bottom with sup A = a and for all
> > x in A, there's some d in L\bottom with d <= a, sup A\x


A weak partition of a point a in a complete lattice L
is some A subset L\bottom for which sup A = a
and for all x in A, bottom /= x inf (sup A\x).

{a} is not a weak partition of a.

> > Definition 3.62.

A strong partition of a point a in a complete lattice L
is some A subset L\bottom for which sup A = a and
for all U,V subset S, (U,V disjoint iff bottom /= (sup U) inf (sup V)).

There are no strong partitions because if U = A and V is empty
bottom = (sup U) inf (sup V).

Where in the heck is Conjecture 4.153? In what section?

> I mean that filter can be partitioned into ultrafilters in the REVERSE
> order.


There is no thorning of a filter by ultrafilters.

Why the names thorning and partition for
defintions that are unrelated to the words.


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.