Références - Normalesup.org

(E, T)
B ⊂ T B
ET1T2
T1T2T1T2T1⊂ T2
T={∅, E}
T=P(E)
d(x, y) = 1x6=y
0x=y

EB
E E ∅
B
∀(B1, B2)∈ B2,∀x∈B1∩B2,∃B∈ B, x ∈B⊂B1∩B2
T
T={ω⊂E, ∀x∈ω, ∃B∈ B, x ∈ B ⊂ ω}
B
B B
B
EGE E ∅
B G
B
E
G
E
K⊂E K
(Oi)i∈I
K⊂[
i∈I
Oi
E
E ? E
E

a∈E(un)nE
(un)na
a∈E(un)na
(un)n
A⊂E E E
A
l l
E
E
Mp(C)
P=Xp+ap−1Xp−1+. . . +a1X+a0∈C[X]p
P
max 1,P0≤i≤p−1|ai|pR
Rp[X]
Mp(R)
Mp(K)K=R C
n∈N∗p∈ {1, . . . , n} Mn(K)
p p
A∈ Mn(C)
A0
A
A(u, Au)u∈Cn
A
A B ∈ Mn(C)
B A
n
R
P∈R[X]n P R
∀z∈C,|P(z)| ≥ |Im(z)|n

n∈N∗K=R C M∈ Mn(K)
λ1, . . . , λn∈C(Pq)q∈N∈n(K)N
P−1
qMPq−→
q→+∞(λ1, . . . , λn)
(λ1, . . . , λn) (λ1, . . . , λn)
F([0,1],[0,1]) [0,1]
[0,1]
[0,1] [0,1]
F([0,1],[0,1])
F([0,1],[0,1])
d1d2E
(E, d1) (E, d2)
k K
kd1≤d2≤Kd1
R
d1(x, y) = |x−y|
d2(x, y) = |x3−y3|
d3(x, y) = min(1, d1(x, y))
d1d2
d1d3
Rd(x, y) = |x−y|
f:R→Rdf(x, y) = |f(x)−f(y)|
d dff
f
R

d df
R
Rdff(R)
E
k·k1k·k2
T1⊂ T2T1T2)
⇔ ∃k > 0,k·k1≤kk·k2
⇔ ∃k > 0, B2(0,1) ⊂B1(0, k)
(E, d)
(Fn)n∈N
0Tn∈NFn
X(On)n∈N∗
X X
Ω := \
n∈N∗
On
X
ΩGδ
X(Fn)n∈N∗X
Γ := ∪n∈N∗Fn
A⊂X¯ A
A⊂X