Liste 4 : Axiomes de séparation

Qα∈AXαXα
α∈A Xαα∈A
x6=y⇒ {x} 6={y}.
{x} 6={y} ⇔ (x /∈ {y}y /∈ {x})
R{]a, +∞[|a∈R}
f:Y→X X
Y
(X, T)T ≤ T 0(X, T)
(X, T)
(X, T)
(X, T) (Y, T)f, g :
X→Y f|D=g|Df=g
S2={(x, y, z)∈R3:x2+y2+z2= 1}
p:S2→R: (x, y, z)7→ x.
RS2Tp
(S2,T)
X f :X→Y
f(X)
X(Y, T)f:X→Y
XTf(X, T)
f
(X, T) (X, T)Y
X f :X→Y f|Y= idY
X Y D X Y f :D→Y
˜
f:X→Y˜ f|D=f

RtR
{(ω× {0})∪(ω0× {1})|ω, ω0∈ E}.
∼
(x, i)∼(y, j)⇔x=y(i=j x 6= 0).
(RtR)/∼R
R
AtB= (A× {0})∪(B× {1})Fα∈ABα=Sα∈A(Bα× {α})