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

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 William Elliot Posts: 2,637 Registered: 1/8/12
Partition of a filter
Posted: Nov 8, 2013 3:21 AM

On Thu, 7 Nov 2013, William Elliot wrote:

> Of course, most mathematicians would skip the section on partitions
> will happen when you use established terms with your novel definitions.
>
> Are these correct?

Here, completely getting rid of that useless weird = sign, are
much better, clearer and direct statements of the definitions.

> 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
> or do you simply mean A is down directed?

A thorning of a point a in a complete lattice L
is a subset A, of L\bottom with sup S = a and
bottom /= x inf y

> Damn that weird, dysfunctional, squished inward equal sign, notation
>
> 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 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, bottom /= a inf (sup A\x)

> Definition 3.62.
> Does A weird= B mean anthing?

A strong partition of an element a in a complete lattice L
is a subset A, of L\bottom with sup A = a and for all
U,V subset A, (U /\ V not empty iff bottom /= (sup U) inf (sup V))

A strong partition of an element a in a complete lattice L
is a subset A, of L\bottom with sup A = a and for all
U,V subset A, (U /\ V empty iff bottom = (sup U) inf (sup V))

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