User:Lord Farin/Sandbox/Nets

Considerations
Basically the confusion over nets boils down to requiring a Definition:Directed Ordering or a Definition:Directed Preordering.

Since Moore-Smith uses the latter, it makes sense to have Definition:Moore-Smith Sequence as a mapping from a directed preorder.

It furthermore makes sense to be completely unambiguous and have Definition:Net be a disambiguation.

It then remains to give a precise name to the directed order variant. This is however not common so we need to be creative.

Since Kelley apparently coined the name "net" and meant the preorder version we cannot just take that for the directed order variant.

All things considered, the proposal is:


 * Definition:Directed Set as a transclusion of ordering/preordering
 * to have Definition:Directed Ordering and Definition:Directed Preordering resp. "-ed Set"
 * Definition:Net as a disambiguation (probably Definition:Net (Order Theory) because there are more things called "net") of ordering/preordering
 * to have Definition:Order Net and Definition:Preorder Net with the latter a redirect to Definition:Moore-Smith Sequence.

What do we have now

 * Definition:Directed Set
 * Definition:Directed Subset
 * Definition:Directed Ordering


 * Definition:Moore-Smith Sequence
 * Definition:Net (Set Theory)
 * Definition:Net (Preordered Set)


 * Definition:Convergent Net
 * Definition:Generalized Sum


 * Categories for the above

Approach

 * Definition:Directed Set transcludes
 * Definition:Directed Ordered Set
 * Definition:Directed Preordered Set
 * Definition:Directed Set/Ordered or Preordered Additional explanatory subpage about directed sets
 * Has Definition:Directed Subset as a redirect target
 * Incoming links to Definition:Directed Set and Definition:Directed Subset are discouraged
 * Definition:Directed Ordering
 * Explanatory subpage
 * Definition:Directed Preordering
 * Explanatory subpage


 * Definition:Net (Order Theory) transcludes
 * Definition:Order Net
 * Definition:Moore-Smith Sequence
 * Definition:Preorder Net as a redirect
 * Definition:Net (Preordered Set) subsumed in this and deleted
 * Definition:Net (Set Theory) deleted
 * Definition:Net (Order Theory)/Ordered or Preordered Explanatory subpage about nets
 * Incoming links to Definition:Net (Order Theory) are discouraged


 * Definition:Convergent Net etc. work on the basis of Definition:Preorder Net = Definition:Moore-Smith Sequence


 * Definition:Generalized Sum and related will have to be completely reworked to match sources. No more questionable error prone generalizations like past versions of me attempted