Mathematical Economics

After some brief discussion of the course's scope and aims, we begun with the definition of a distance function (metric) w.r.t. a non empty set of reference as a real function defined on the product of this set with itself that satisfies positivity, separation, symmetry and triangle inequality. The example of the discrete metric showed that any such set bears at least one such function, and further examples implied that more than one metrics can exist, possibly inside structured families, some of which attribute possibly different properties to the reference (or carrier) set. The structured set comprised of the carrier set with the metric was defined as a metric space.  We went through with the examination of several examples of such spaces. We examined the important example of the space of bounded real functions on a non-empty domain endowed with the uniform metric and hinted that it contains as particular example spaces of real n-vectors equipped with the max-metric.

We have shown that it is possible that different metrics on the same carrier set can obey relations. We suspected that such relations might imply analogous ones between the relevant properties that each metric endows the space with, and that provides as with a motivation of further examination of such relations.

Details can be found at the course's syllabus, notes on the previous here, and a counterexample of a metric here.