Mathematical Economics

We concluded our examination of the notion of total boundness by considering issues involving metric comparisons and finite products. We provided several remarks regarding hereditarity, etc, that implied that the notion coincides with that of boundness on Euclidean spaces.

We begun the examination of topological notions on a metric space that arise by the presence of a metric. We initially defined the notion of open and closed subsets as duals, then the subsequent notion of a topology arising from a metric, and then generalized the notion in order to see that there exist topologies that do not arise from metrics (e.g. the indisrete topology when the carrier set has more than one elements). We have that when a topology arises from a metric is termed metrizable (e.g. the discrete topology that arises from the discrete metric). The issue of metrization of a topology is essentially settled by the Nagata-Smirnov theorem that is completely outside the scope of the course.

You can find notes for the above here and here.