Mathematical Economics

During the second TA session we were proeccopied with the following:

First, we revisited and corrected exercise 8 of the problem set 1 that was erroneously solved during the first TA session (find the solutions here).

Secondly, we proved two lemmas. The first concerns total boundness and finite product spaces, already seen in class. The proof is analogous to the proof of boundness and finite products. The second concerns the equivalence of characterising continuity using open balls or neigbouring systems (not yet seen in class).

Third, we did not have enough time to solve two exercises. The first is exercise 2 of problem set 3 and it regards the non-total boundness of unit balls on the square integrable functional space. Its solution employes Riesz's Lemma (a short proof of which you may find at O'Searcoid's textbook (see Sylabus) ch. 12), and the Pigeonhole Principle (a principle of Discrete Mathematics). The second, exercise 4 of problem set 3, regards the continuity of metric functions. Its solution is relatively straightforward.

You may find the matterial covered (and not) during the TA session here.