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28 Nov 2018: b) Use the Mayer–Vietoris sequence to compute the homology of Σg#Sn, andhence deduce that it is homeomorphic to Sn2g. ... Show that the linear map A : R2 R2 preserves the equivalence relation (a,b) (a′,b′) (aa′,b b′) Z2,and so induces a

2 Mar 2018: Exemple 3.1.2.(i) Si B est un espace topologique et F un espace discret, alors p : (b,f) B F 7 b B est. ... x) est le stabilisa-teur de x pour l’action de Π1(B,b) sur p1 ({b}).

4 Apr 2018: and Δ : B B B are monoidmorphisms, where B B is a monoid with the structure described earlier. ... χ: [A, B] [A′, B] [A A′, B B] [1,μ] [A A′, B] χ0 : I = [I, I] [I,ι] [I, B].

9 Oct 2018: 10. Let f : X Y. Let A, B X and C, D Y. ... For each of claims (a)–(f) below, give aproof or counter-example. (a) f(AB) = f(A)f(B) (b) f1(C D) = f1(C)f1(D)(c) f(AB) =

28 Nov 2018: A group (G, ,e) is abelian2 if for all a,b G we have a b = b a. ... f ′(f(z)) =a′(azbczd) b. ′. c′(azbczd) d′. =a′(az b) b′(cz d).

20 Dec 2018: ii) Let A = {1, 2, 3, 4, 5, 6} and B = {0, 1}. ... If c, c̃ : A B are given byc(0) = 0 c̃(0) = 0.

16 Jul 2018: results in [WZ17b]. After the classification result (Theorem B), the chapter continues with conse-. ... phic profinite completions, then they are commensurable. Following this we will use the techniques from Theorem B to investigate two other.

8 Oct 2018: 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 R}. ... 11. Let X = Rd endowed with the σ-algebra B of Borel sets.

6 May 2018: Si B(a,r) B(b,s) 6= , alors B(a,r) B(b,s) ou B(a,r) B(b,s). ... On se donne b′ {0, 1,. ,pn 1} t.q.b b′ mod pn.

26 Apr 2018: Démonstration. Soit x : R Rd une solution de ẋ(t) = b (x(t)). ... A′. 7 iest une injection continue. Autrement dit :. A B = B′ A′.