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21 May 2005: 8. Part (b) is incorrect: In the figure, the segments labelled A are supposed to beidentified and the segments labelled B are supposed to be identified, but theresulting segments A and ... a},{1, 2, 5}, {1, 2, 6}, {1, 3, 4}, {1, 5, 6},{2, 3, 5}, {2, 4, 6}

18 Jan 2005: Lïiì Õ Þòð;ñ;à Õ Ð5 Ðîbª5àÏTÐbÑÑEÑEÐàÒ Â5ËE»b«»b¿ª¥bÔwb¿ ¥ÂµwEÁmY«=ª¥«'á;Sû!YE»lª=5bi=T¥«=µ¥ ðSÔw}Á'TþwEÁÁEíYE=¥i¥w bªEÁmª¥@¥Âµ(ðÔs«=ÓªEüÖwE¿ª@ªÁm¥w¥Âµ¥w¥«=

12 Apr 2005: If B B, then fB(ω) is definedto be the value of f(φ) for any φ with φ(A) = ω(B). ... 3.1 as follows. Let K1 be the chain of all subsets of all sets B B.

8 Dec 2005: say with active coordinate set I, such. that for all a [m]n and all b, b′ L{L+}, we have c(a, b) = c(a, b′) = c′(a),say. ... ii) A B U if and only if A U or B U;.

21 May 2005: 6. If A and B are subsets of Rn, we write A B for the set {a b : a A,b B}. ... Show that if Aand B are both closed and one of them is bounded, then A B is closed.

21 May 2005: 6. If A and B are subsets of Rn, we write A B for the set {a b : a A, b B}. ... Show that if Aand B are both closed and one of them is bounded, then A B is closed.

14 Mar 2005: Proof. Define B [N]2 to be the set of all (x,y) such that xy A. ... labelling vertices of a cube (as they would if a, b and c denoted three orthogonal vectors.

23 Nov 2005: 3. The symmetric difference of sets A and B is A 4 B = (A B) (B A). ... 8. Define a relation R on N by setting aRb if a divides b or b divides a.

21 May 2005: BA. B. B. B. A A D. A. DCC. AA A A. ... 3. (b) Now show that γ is an epimorphism (i.e., is surjective).

21 May 2005: B. C. C. B. B. C. C. B. C. C. B. ... B. C. C. B. B. A. A. A. A. A. A.

21 May 2005: BA. B. B. B. A A D. A. DCC. AA A A. ... 4, 5, 6} }. B B. AA. 2. 1. 2. 1. 3 4. 65. defines a simplicial complex that is a pseudo 2-manifold but not a 2-manifold.

21 May 2005: Every continuous function on a compact interval [a,b] can be uniformly approximated bypolynomials (Weierstrass’ theorem). ... 12. Let B = B(0, 1) denote the open unit disc, C = C(0, 1) the unit circle and D the set{z C | |z| > 1}.

21 May 2005: ZWYO v b o _p_a{C?x<Y<WY{rpYd¥Wb v <WMC_c l hn >A h uWYbdxx<Y+{ } bd]Z&_]ª{Yx_Y+{_{{pp? ... oc| _a&# nÌ ¿ Â b vv br o Z| bdÒbd&<r_c] x<Y+d{bd]?

21 May 2005: 4. Which of the following subsets of R2 are (a) open, (b) closed? ... 1. 2 ANALYSIS II EXAMPLES 2. 7. If A and B are subsets of Rn, we write A B for the set {a b : a A,b B}.

4 Nov 2005: 4. Which of the following subsets of R2 are (a) open, (b) closed? ... 1. 2 ANALYSIS II EXAMPLES 2. 7. If A and B are subsets of Rn, we write A B for the set {a b : a A,b B}.

21 May 2005: A B = {a b : a A, b B}, AB = {ab : a A, b B}. ... It shouldbe clear that. b. af > 0, and you should explain why this is so.