Mathematical Economics

We continued the examination of issues involving convergence and continuity. After a little bit of trouble, we have provided with an application that establishes the continuity of the sup functional when properly restricted to possibly non-empty metric subspaces of the set of bounded real functions equiped with the uniform metric. Using this and under further assumptions we were occupied with the issue of convergence of approximate maximizers under uniform convergence of their respective criteria. You can find here notes for the above. We note that the topology generated by the uniform metric might be unecessary strong for the examination of the asymptotic behavior of sequences of maximizers, and a weaker topology for this, is the one of hypo-convergence.

We have begun the examination of the non-topological notion of completeness of a metric space. You can find here notes for it.