Mathematical Economics

We continued with the examination of the notion of total boundness. We proved that it is a refinement of the notion of boundness, in the sense that total boundeness implies boundness, while we refered to their equivalence in Euclidean spaces. We were occupied with the issues of  the equivalence of metrics w.r.t. total boundness, and the invariance of the notion w.r.t. finite products.

We begun the examination of topological notions on a metric space that arise by the presence of a metric. We defined open and closed subsets as duals, and considered the collection of open subsets as a topology generated by a metric. We were occupied with the issue of when two metrics define the same topology. We begun the study of the concept of sequential convergence.