1. An invariant of a process (phenomenon, transformation, etc.) is a numerical parameter whose value remains constant during that process. Analogously, a covariant is a parameter whose numerical value has only in a (relative) sense a preselected coordinate system but changes in a specified way if the coordinate system is changed (e.g. given by some symmetry transformation).
2. Investment Science;Luendbeger,1998
3. Most of the axioms take the same form as in standard models because they simply define market organization.
4. We could also take the empty basket into consideration but this would spoil the projective space interpretation.
5. Note that this means that we treat all taxes, brokerages, etc. as liabilities and therefore as separate assets. In this way we are not forced to consider friction in the model. Models that have scale effects (projective symmetry is broken) should have a dual description in terms of non-transitive quotations.