TD4. Rappels de topologie. Ensemble de Cantor.

X Y f :X→Y
f
f
x X f f(x)x
E A B
B A B ⊂A
x∈B A B
A B B C A
C
K F ⊆K F
ROR
Ω∪]a, +∞] Ω ∪[−∞, a[aRΩOR
[0,1]
R
E A ⊂E A 6=∅d(x, A) = infy∈Ad(x, y)
x7→ d(x, A)
x∈E d(x, A) = d(x, A)
x d(x, A)=0
(An)n∈Nn An
Tn∈NAn=∅
F0:= [0,1]
∀n∈N, Fn+1 := Fn
3∪2 + Fn 3
F∞
F∞
F∞
F∞
F∞x∈F∞V
V∩F∞={x}
F∞R
F∞2N