I have continued my work on Belton http://www.maths.lancs.ac.uk/~belton/www/notes/fa_notes.pdf. I had done Tychonov’s Theroem for finite collections – here I saw the proof for the general case. I looked at the Banach-Alaoglu Theorem (the closed unit ball in the dual space of a normed vector space $X$ is compact in the weak* toplology). I saw that every normed vector space is isometrically isomorphic to $C(K)$ for some compact, Hausdorff space $K$. I looked at topological vector spaces and convexity. Finally I looked at the Krien-Milman Theorem (in a locally convex topological space $X$, every non-empty, compact, convex subset of $X$ is the closed, convex hull of it’s extreme points: $\overline{\text{cnv}}\partial_e C$). I have done the first two questions 5.1, 5.2.