Liste 5 : Compacts et connexes

S2
p: (x, y, z)7→ x
(Rn,E)xm→x{xm|m∈
N}∪{x} {xm|m∈N}
X=N∪ {√2}
T={U⊂X|√2/∈U X\U}.
TX(X, T)
X A X TX
X A (X, T)
(X, T)K
(X, T)K
(X, T)B T (X, T)
XB
R2dSN C F
dSN C F (x, y) = d(x, y)x=λy, λ ∈R
d(x, 0) + d(0, y).
(X, T)X
{0,1}
(X, T)
f:X→Ra, b, c ∈Ra, b ∈f(X)a≤c≤b c ∈f(X)
(X, T)
(X, T)
X= ({0} × [−1,1]) ∪([−1,1] × {0})T
R2(X, T) (x, y)
X X\{(x, y)}