A coordinate space represents (among other things) the domain space of a table.

Corresponding to each coordinate space will be a set of objects of the following kinds:

Position -- The elements of the coordinate space.

Mapping -- (Add a description.)

OrderSpec? -- The ways of specifying partial orders of this coordinate space''s Positions.

XuRegion -- An XuRegion represents a set of Positions. The domain of a table is an XuRegion.

When defining a new coordinate space class, one generally defines new correspoding subclasses of each of the above classes. A kind of any of the above classes knows what coordinate space it is a part of (the "coordinateSpace()" message will yield an appropriate kind of CoordinateSpace). CoordinateSpace objects exist mostly just to represent this commonality. Coordinate spaces are disjoint -- it is an error to use any of the generic protocol of any of the above classes if the objects in question are of two different coordinate spaces. For example, "dsp->of (pos)" is not an error iff "dsp->coordinateSpace()->isEqual (pos->coordinateSpace())".

All of the instance variables for CoordinateSpace are basically cached quantities that require vary little actual state from the derived classes in order to be constructed. This realization allows a knot to be untangled when reading these objects from external storage.