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24 Feb 2014: 9. Show that Hausdorff distance dHaus(A,B) defines a metric space structureon the set of compact subsets of a given metric space. ... Recall dHaus(A,B) = inf{δ |A Uδ(B),B Uδ(A)}, where Uδ denotesthe metric δ-neighbourhood.].

16 Jul 2014: symplectic structure as before. Torus bundle X (B) B Torus bundle X̌ (B) B. ... Kähler form 2īK. complex coordinates x̌i K/yi. Torus bundle X (B) B Torus bundle X̌ (B) B.

20 Oct 2014: 14. Let A and B be subsets of Zp of size αp and βp respectively. ... Prove that there existu,v Zp such that. |A (uB v)| αβp αβp, where uB v denotes the set{ub v : b B}.

19 Dec 2014: Let a = min{| A |: A is an infinite maximalalmost disjoint family of subsets of ω}, b = min{| B |: B is unbounded in (ωω,)},and d = min{| D |: D is dominating in ( ... i) Prove that 1 min{a, b, d} max{a, b, d} 20.

18 Sep 2014: Lemma 3.3 Let B = b I be a Möbius band in X. ... Then λ must intersectsome band B = b I in at least 5 vertical segments.

19 Dec 2014: Forcing and Partial Isomorphisms. Suppose that A and B are τ –structures in a vocabulary τ. ... forth set for A and B :. (f F)(a A)(g F)(f g a dom(g)) and(f F)(b B)(g F)(f g b range(g)).

2 Jan 2014: F (a, b) = b F (c, d) = 1 d. ... compositions. The most tricky is the composition a (b, c) but direct calculation.

18 Sep 2014: Proof. Let C be such that the Γ-translates of B(x0,C) cover X. ... Consider a triangle (x,y,z), contained in a ball B = Bx(R).

10 Oct 2014: r)a and r b := θ2(r)b for a A,b B so r(ab) = θ1(r)ab = aθ2(r)b. ... property. A A R B B. C. α. α′. φ. β. β′.

16 Apr 2014: We can find minimalprimes p′A A, p′B B such that p′ = (p′A,p′B). ... Let B = Â. Then:. 1. For each minimal prime q B, B/q is O-flat of dimension d 1, and B/(λ) is generically reduced.