Partial order/Talk

The Alexandrov topology can be defined for any partially ordered set. Here, a set is open iff it is upwards closed. However, there are other topologies of interest for varied types of partially ordered sets, so I doubt that it is "standard". -JB

The most common and easy to read graphical representation of partial orders is in my opinion not DAGs but Hasse diagrams. In this type of diagrams the direction of the order is implied by the relative positioning of the elements. If there is an arc from x to y and y is above x on the paper then x<=y.

Would you like to add those two bits of information? Be bold in updating pages :-) --AxelBoldt

Ok, I took the oportunity to add some other things. -JB

Thanks! Could you also explain the notion of "upwards closed subset"? --AxelBoldt

Which relation does "is a subobject of" refer to? -OJarnef

I think it probably refers to relations such as "is a subgroup of", "is a subspace of", "is a subring of" etc.; the term "object" is used in the sense of category theory here. --AxelBoldt