204:connexité.Exemples et applications.

X
X
X
X
X{0,1}
X A
Q R R2
X X
(a, b)f[0,1] X f(0) = a f(1) = b
Rn
R2
X ε x y
ε x y
X¯ X
¯
X
Ai
AiAi0SAi
Ci−1∩Ci6=∅

⇒ ⇒ ⇒ ⇒ ⇒
⇒
sin(1/x) [0,1]
R2
R2R2
Q
S+
n(R)S++ n(R)
E⇒E
Rn
GLn(C)
Sn(R)
Hn(C)
x y x y
X x y
x x
GLn(R)
Q

E
R
R R2R R2
R1RmR
Rm
Rn
f a
f
E F
C1U F
f U f(U)
f
f
U
U
RnRnC1
Rnf∀x df(x)
UCf
f
f U
U
1/z 0 2iπ
f U
f
U
f g U
f g
g U g f U

x0=f(t, x)x(0) = x0∈
F F
Rniut−∆u=P(u, ¯u)
u(0, x) = u0(x)∈Hs(Rn)P s < n/2
C0(I, Hs)I
SO3(R)