.
.
.
1) : S=xy.
2) x,y,z: V=xyz.
3) , U R I U=RI. U R , I U R: I= .
Rn n (1,2,,n). n- n- .
=(1,2,,n), =(1,2,,n). 1,2,,n .
. =(1,2,,n) =(1,2,,n):
d(x,y)= (1)
:
1) d(x,y)³0, , d(x,y)=0 Û =, .. xi=yi "i=1,2,,n.
2) d(x,y)=d(y,x) .
3) d(x,y)£d(x,z)+d(z,y) "x,y,zÎRn ( £ + ).
a(1,2,,n) Rn R>0 . x(1,2,,n):
(a,R)={xÎRn: d(x,a)<R} - () R.
(a,R)={xÎRn: d(x,a)£R} () R.
S(a,R)={xÎRn: d(x,a)=R} Rn.
, Rn:
=R (2)
. a1,,an b1,,bn , a1<b1,,an<bn. M(1,2,,n)ÎRn,
.
M(1,2,,n)ÎRn,
.
(,, ) .
R>0 0(,, ) . (, 0(,, )).
. Rn. , R>0 , R (0,,0).
. ()ÌRn.
{x1} - , Î,
..
{xn} - , n- Î.
, () , {x1},..., {xn}.
. . () . , R>0 , d(M,O)<R "M(x1,,xn)ÎE.
0£êx1ê£ <R, , 0£êxnê£ <R "M(x1,,xn)ÎE
, {x1},..., {xn} .
. {x1},..., {xn} . , $>0: êx1ê<C, ,êxnê<C "M(x1,,xn)ÎE. <C =R
|
|
.., d(M,O)<R "MÎE. , . ...
. , .
.
1) Rn Æ - .
2) ().
3) ().
0Î ÌRn, , 0.
. FÌRn , Rn (.. Rn\F ).
, , . .
.