Course : Mathematical Economics

Dear Students,

In the first tutorial, we stated the definitions of a metric and a pseudo-metric and we solved exercises 4.8 and 5 from Problem Set 1 (it can be found in the folder TA Sessions 2023-2024 -> TA Session 1). We also presented an example of a metric reflecting the structure of a graph. Specifically, if the graph is connected, the metric is well-defined as the minimum distance between any two vertices of the graph. The relevant notes are here. 

In the second tutorial we discussed the definition of a bounded function from a non-empty set X to a metric space Y, and we showed that the set of such functions, B(X,Y), together with the uniform metric, is a well-defined metric space. Moreover, we proved that the boundedness of the metric space Y is inherited to the functional space B(X,Y) (exercise 7, TA Sessions 2023-2024, Problem Set 2). From the same Problem Set, we solved exercises 3, 4, and 6. We also noted that in any metric space (X,d), the boundedness of a subset A, is equivalent to the condition: d(x,y) <= e, for some e>0, for all x,y in A.

You are advised to try exercises 6, 7 and 8 from Problem Set 1, as well as exercises 1, 2, and 5 from Problem Set 2.

Feel free to reach out for any questions.

Pantelis