BI TP - L THUYT O V TCH PHNBi 1: Chng minh rng mt lpCnhng tp con caX l mt i s khi v ch khiCkhng rng v a) , AC B C A B C b)CAC A C Bi giiBi ny ta chng minh hai chiu nh sau:() Gi s X l mt i s, ta chng minh hai tnh cht a) v b) trn.+ Ta c, , \CX A C A X A C (chng minh xong tnh cht b)+ p dng nh ngha ta c: , , \ ( )( ) (thoa a)c c c c c cc c cA C B C AB C A B C X A B CA B C A B C() Ga s ch khiCkhng rng tha mn, AC BC A BC vCAC A C , ta chng minh X l i s. Tc l,1. , A C B C A B C2. , \ A B C AB CTht vy, + , ,( ) (( ) )(thoa 1).c c c cc c cA C B C A C B C A B CA B C A B C A B C+ , \(thoa 2)c cA B C B C A B C AB CVy bi 1 c chng minh xong.Bi 2: Cho( )kkf l mt dy nhng hm o c, c bn theo o trnA, ngha l vi mi0 > , vi mi0 > , tn tiN sao cho{ }: ( ) ( ) , ,k lx Af x f x k l N < Chng minh rnga) Tn ti dy( )n nk cc s t nhin sao cho11 1: ( ) ( )2 2i ik ki ix Af x f x+ 102i, vi mi >102i, tn ti( ) N isao cho1 1: ( ) ( ) , , ( )2 2k li ix A f x f x k l N i < >' ; Ta xy dng dy con ( )ik if ca ( )k kf bng cch ly cc ch s ki sao cho1 2 11(1), max{ 1; (2)},..........max{ 1; ( )}i ik k k k kk k k i + +Khi ,11 1: ( ) ( )2 2i ik ki ix Af x f x+