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  2. Cubulating spaces and groups; example sheet 1 Macarena Arenas ...

    https://www.dpmms.cam.ac.uk/~mcr59/index_files/examplesheet1.pdf
    29 Jan 2024: b b. bb. b. b. b. b. b b. b. b. ... b b. b. b. 6. Let Γ and L, respectively, be the graph and the link pictured below.
  3. Mich. 2023 ANALYSIS AND TOPOLOGY—EXAMPLES 4 PAR 1. Let ...

    https://www.dpmms.cam.ac.uk/~par31/at/4.pdf
    21 Nov 2023: b) Define an equivalence relation on X Y by (x,y) (x′,y′) iff x = x′. ... D2f exists at (a,b). Show that f is differentiable at (a,b).
  4. Lent Term 2024 O. Randal-Williams II Algebraic Topology // ...

    https://www.dpmms.cam.ac.uk/~or257/teaching/IIAlgTop2024/Sheet4.pdf
    11 Jan 2024: Show that the linear map A : R2 R2 peserves theequivalence relation (a,b) (a′,b′) (aa′,bb′) Z2, and so induces a continuous map fAfrom the torus T to itself.
  5. Lent Term 2024 O. Randal-Williams II Algebraic Topology // ...

    https://www.dpmms.cam.ac.uk/study/II/AlgebraicTopology/2023-2024/Sheet4.pdf
    16 Jan 2024: Show that the linear map A : R2 R2 peserves theequivalence relation (a,b) (a′,b′) (aa′,bb′) Z2, and so induces a continuous map fAfrom the torus T to itself.
  6. Mich. 2023 ANALYSIS AND TOPOLOGY—EXAMPLES 4 PAR 1. Let ...

    https://www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2023-2024/4.pdf
    24 Nov 2023: b) Define an equivalence relation on X Y by (x,y) (x′,y′) iff x = x′. ... D2f exists at (a,b). Show that f is differentiable at (a,b).
  7. Michaelmas Term 2023-24 Numbers and Sets: Examples Sheet 4 ...

    https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2023-2024/numset4_2023.pdf
    16 Nov 2023: 3. The symmetric difference of two sets A and B is A4B = (AB) (B A). ... 8. Define a relation R on N by setting aRb if a divides b or b divides a.
  8. SS (ss2871@maths.cam.ac.uk) Michaelmas 2023 Probability and Measure 1 …

    https://www.dpmms.cam.ac.uk/study/II/Probability%2BMeasure/2023-2024/ex1.pdf
    11 Oct 2023: algebra. 1.2. Show that the following sets of subsets of R all generate the same σ-algebra:(a) {(a,b) : a < b}, (b) {(a,b] : a < b}, (c) {(,b] : b ... 1.8. Let B be a Borel subset of the interval [0, 1].
  9. Mich 2023 FUNCTIONAL ANALYSIS – EXAMPLES 3 AZ 1. ...

    https://www.dpmms.cam.ac.uk/~az10000/2023-mich-partiii-func-anal-sheet3.pdf
    14 Nov 2023: 10. Show that B = conv Ext B but that BC[0,1] 6= conv Ext BC[0,1]. ... 16. Let X,Y be Banach spaces and T B(X,Y ). Assume that T(X) is closedin Y.
  10. Mich 2023 FUNCTIONAL ANALYSIS – EXAMPLES 2 AZ 1. ...

    https://www.dpmms.cam.ac.uk/~az10000/2023-mich-partiii-func-anal-sheet2.pdf
    28 Oct 2023: a,b]. )= ba for all a < b in R. 18. ... Showthat (K,M,µ1) is the completion of (K,B,µ). 19. Let X be a real or complex vector space with a topology such that addition, scalarmultiplication are continuous, and
  11. Example sheet 1 Example sheet 1 Problem 1. Show ...

    https://www.dpmms.cam.ac.uk/study/IB/Optimization/2022-2023/example1_easter23.pdf
    17 Jul 2023: a) minimize cT x subject to Ax = b. (b) minimize cT x subject to Ax b. ... d) minimize cT x subject to Ax b, x 0. In each case.

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