Mathematical Economics

We were occupied with the comparison of topologies generated by different by different metrics that obey functional inequalities.

We begun the study of the concept of sequential convergence given the notion of a neighborhood system of a point in a topological space and we have proven that in a metric space the notion can be equivalently described via the subsystem of open balls centered at the limit. We have proven that a sequence inside a metric space can have at most one limit, due to the property of separation. The consideration of the behavior of sequences in indiscrete topological spaces implied once more that there exist topologies not generated by metrics. We used the aforemntioned comparison of topologies in order to compare the convergence properies w.r.t. the aforementioned metrics that obey functional inequalities. 

Given the notion of sequential convergence we begun to examine of the notion of continuity of functions between metric spaces.

You can find notes for the above here and here.