Mathematical Economics

Given the examination of the non-topological notion of completeness of a metric space that was made available in the previous tutorial we were occupied with the issue of completeness (w.r.t. the relevant uniform metric) of a bounded function space when the range is a complete metric space. You can find notes for the aforementioned notions here (remember that the part of the proof of the latter result concerning the boundness of the limit of the relevant Cauchy sequence was left as an exercise).

We have also studied the stronger than topological continuty notion of Lipschitz continuity, obtaining finally the notion of a contraction. You can find for those notions here. We are now almost ready to study our first fixed point theorem.