X = C(I, R)
I = [0, 1] R
dsup(f, g) = sup{ | f(x) - g(x) | : x " I}
B = {f " C(I, R) : f(1) = f(1) }
2
C(I, R) dsup
T AK B NIE
X
X
X
X
dsup
x, y " R2 I(x, y) x y
1 1 1
a0 = (0, 0) a1 = (1, 0) bn = (1, ) cn = (n, ) n = 1, 2, . . .
n n2
" "
Y1 = I(a0, cn) Y2 = I(a0, bn) *" I(a0, a1)
n=1 n=1
Y3 = Y1 \ {(0, 0)} Y4 = Y2 \ I(a0, a1) = {(x1, x2) " Y2 : x2 > 0}
i = j Xi Xj

Q
Y1, Y2, Y3, Y4
" 1
Y1 = (Q × R) *" ([0, 1] × {0}) Y2 = ({0} × R) *" ({n} × R) *" ([0, 1] × {0})
n=1
"
3
Y3 = Y1 \ {( , 0)} Y4 = Y1 \ {(1, 0)}
3 3
Y1 Y2
B ‚" [0, 1]
s " [0, 1]
s
n (s, ) (0, 0)
n
B
s " [0, 1]
 (X, d)
(X, d)
(X, TX)
(Y, TY )
f : X Y (X, TX)
(Y, TY ) p : X × Y X
(X, TX) (Y, TY ) X
(X, TX)
f, g : X Y
(X, TX) (Y, TY )
a (X, TX)
Ä…, ² a X
T = {(t, sin(1)) : t " (0, 1]} *" ({0} × [-1, 1])
t