
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 > for already knowing about them. That and other misunderstanding > 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))

