TD6. Rappels de topologie. Ensemble de Cantor. Échau ements

? X Y f :X→Y
f
f
x X f f(x)
x
(An)n∈N
n AnTn∈NAn=∅
E A
B B A B ⊂A
x∈B A
B
A B B C A
C
(un)n∈N
l K ={l} ∪ Sn∈N{un}K
? 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

?
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
R R
P(R)R
L
F∞P(F∞)⊂L⊂ P (R)
F∞Card (P(F∞)) =
Card (P(R)) Card (L) = Card (P(R))
R