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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. 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.
  9. A Brief Guide ToMathematical Writing This guide is intended ...

    https://www.dpmms.cam.ac.uk/~grw46/Writing_Guide.pdf
    11 Mar 2024: f(B) then y = f(a) for some a A andy = f(b) for some b B but then f(a) = y = f(b) so a = b A Band y ... A B), so f(A) f(B) f(A B) and the sets are equal asrequired.
  10. 8 Borel functional calculus and spectral theory Throughout H ...

    https://www.dpmms.cam.ac.uk/~az10000/2023-mich-partiii-func-anal-spectral-theory.pdf
    28 Nov 2023: Operator-valued measures. A resolution of the identity of H over K is amap P : B B(H) such that. ... By (2), the sequence. (Φ(sn). )is Cauchy in B(H), and hence.
  11. NUMBER FIELDS, LENT 2024 PÉTER P. VARJÚ Disclaimer,…

    https://www.dpmms.cam.ac.uk/~pv270/NumberFields.pdf
    8 Mar 2024: Indeed, the minimalpolynomial of a/b with gcd(a,b) = 1 is xa/b. ... OK =. {a b 1 m. 1/2. 2: a,b Z. }if m 1 mod 4.

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