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4 Nov 2005: Show that E is finite dimensional. 20. Let E be a normed space.

21 May 2005: 16. 17. 18. 19. 20. 212223. 24. 25. D. C. D.

22 Nov 2005: 20. Suppose that (X,d) is a complete metric space. Let U X be a proper open subset withcomplement A = X U.

21 May 2005: 4 ANALYSIS II EXAMPLES 4. 20. [Tripos IB 93301(b)] Let (X,d) be a metric space without isolated points (i.e.

21 May 2005: . . . 20. Let P2 = P2(x,y) be the space of polynomials in x,y of degree 2 in each variable.

21 May 2005: 20. Show that the dual of the space P of real polynomials is isomorphic to the space RN of all sequences ofreal numbers, via the mapping which sends a linear form

27 Oct 2005: 20) (i) Construct a [7, 8, 4]-code from Hamming’s code.(ii) Prove that A(n, d) 2A(n 1, d).(iii) Prove that if d is even then

21 May 2005: 20) Let G have n r 1 vertices and tr1(n) 1 edges.(i) Prove that for every p in the range r p n, G has a subgraph of order

21 May 2005: Show that satisfies the triangle inequality. Is it a metric? 40) Rephrase your solution to Question 20 (on coin weighing) in terms of conditionalentropy.

21 May 2005: 20. An n n magic square is a square matrix whose rows, columns and two diagonals all sum to the samequantity.