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28 Nov 2003: 1. Does there exist an uncountable family B of subsets of N such that for every A,B B(distinct) the intersection of A with B is finite?

29 Sep 2003: 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.

25 Jul 2003: α β) Z. Without loss of generality we can assume that R = [0, a] [0, b]. ... 9. which shows that at least one of a and b is an integer.

26 Jun 2003: Thus if f : A B and g : A′ B′ in apremonoidal category K then the two evident morphismsA A′ B B′. ... Naturality in B (Right Tightening).If f : A U B′ U , g : B′ B then.

17 Jul 2003: Equations for X(5). Let 0 = (0 : a : b : b : a). ... Since B consists of primes p 0, 1 (mod n) it follows by class fieldtheory, specifically the Kronecker-Weber theorem, that 〈B〉 has dimension |B|.Thus [B]=〈B〉 as

20 Jan 2003: Divide I0 into two intervals:. [a, 12 (a b)] and [12 (a b),b]. ... When a or b is infinite we get the unbounded intervals:(,b), (,b], (a,), [a,) or (,).) Firstly, it is clear that X [a,b].

21 Aug 2003: Naturality in B (Right Tightening):If f : A U B′ U , g : B′ B then. ... trB′. AA′,BB′ ((f A′) B′; α; B σ; α1; (B B′) g) (struct)= trA.

7 Oct 2003: Observe that arrows B : B 1 and A : A 1determine functors B : C C/B and ΣA : C/A C. ... X B //. X. X. B. B // 1. 4. We can therefore write BX = X B.