(xn) X x " X
d(xn, x) 0
limn xn x > 0 n0 n e"
n0 xn " K (x)
x (xn) (xn)
x x > 0 n xn " K (x)
1
fn(x) = x C([0, 1])
n
fn(x) = xn C([0, 1]) L1()
X Y
f : X Y x " X (xn)
x X limn f(xn) = f(x)
f : X � X Y x y
(xn) (yn) x y X limn f(xn, yn) = f(x, y)
(xn)
> 0 n0
m, n > n0
d(xm, xn) < .
1
xn =
n
R [0, 1] (0, 1)
(X, d) d
 U x " U > 0
K(x, ) �" U
F
A x " A
> 0 K(x, ) �" A
A A int A U
intU = U