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.

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