Relation Notes

In theory, every kind of relationship we might wish to define between sets is simply a mathematical relation. In fact, even fields are relations between sets representing the base space of the field and sets representing the set of possible values the field can attain over its base space.

In practice, we have need to distinguish between different kinds of relations. Of course, fields are characterized as fields. However, for relationships between sets, we define two special cases; subset relations and topology relations. A subset relation identifies that two sets are related to each other, one the subset of the other. Furthermore that subset is identified by enumerating those members of a collection in the superset that are also in the subset. For example, to specify a processor subset of a whole, we might identify all those elements on the whole that are on the processor.

The other kind of relation we define is a topology relation. Another good name might have been mesh relation. However, we have tried to avoid words, like mesh, that might have specific and overloaded meanings across the various application domains SAF is designed to support. A topology relation defines how different members of a collection are knitted together to form some larger piece. For example, a topology relation is used to define how different elements are knitted together (at the nodes) to form a finite element mesh.