? EBc&VDMJE bW ￥K? ?? 5 &VDMJE bW ￥'? ?  1. ￡ ü? ? 11.1.1  ? ?@???a??? ???? Tb ￡  aA ?μ | 7 O |?≥xy0 ?=xy||0? (1,2,,) ii x yi n==l ? =x yb (b) ?  ??l°¤ V¤ |||?=?xy yx|b (c) ?? 22 2 2 1111 () ( ) 2 0 nnnn ii i ii i ft a tb t b t ab a ==== =?= ? +≥ ∑∑∑∑  ?[1?  ? Q ?[ T￥ ?Y Tμ 2 22 111 0 nnn ii i i ii ab a b === ?? ?≤ ?? ?? ∑∑∑  ' 2 11 nnn ii i i ii ab a b === ≤ ∑∑∑ 2 1 b 2 1 n i= ∑ ? ^ 22 111 () 2 nnn ii i ii i ii ab b ab a === += + + ∑∑∑ 2222 1 n i i a =111 2 nnn iii iii bab === ≤+ + ∑∑∑∑ 2 22 11 nn ii ii ab == ?? =+ ?? ?? ∑∑  ' 2 1 () n ii i ab = + ∑ 22 11 nn ii ii ab == ≤+ ∑ ∑ b 7 5μ , iiiii axybyz=? =? i 22 11 || () ( nn ii ii )x za == ?= ? = + ∑∑ xz b 1 22 11 nn ii ii ab == ≤+ ∑ ∑ =|| ||? +?xy yzb 2. ￡ ü ? n R ?￥?  l ?5 K ^·B￥b }{ k x ￡ L ! ?x y? ^?  { } k x ￥K5 0ε? >  11 ,:| k NkN |ε??> ?<xx  22 ,:| k NkN |ε??> ?<xy b ? ^? H? ? 12 max{ , }kN> N 2||| || | kk ε? <?+?<xy x x x y  ?? ε ^ ?i? ? ?[ =x y'K ^·B￥b 3. ! n R ?￥?  ? l ?￡ ü? ?? L ?}{ k x }{ k y βα, ? ? ? T )(lim kk k yx βα + ∞→ = α k k x ∞→ lim + β k k y ∞→ lim b ￡ ! x ∞→k lim k = x y ∞→k lim k = y5 0ε? >  11 ,:| k NkN |ε??> ?<xx  22 ,:| k NkN |ε??> ?<yy  ? ^? H? ? 12 max{ , }kN> N |( ) ( )| | || | | || | kk k k α βαβα β?≤?+?x+ y x+ y xx yy(| | | |)α βε< +  ?[ )(lim kk k yx βα + ∞→ = α k k x ∞→ lim + β k k y ∞→ lim b 4. p/  2 R ?0"￥ =?aH?D>  1 S = }0,0|),{( ≠> yxyx   2 S = ?  22 0|),{( yxyx +< }1  3 S = ?{ xyx <0|),( } 1 sin,1 x y = b 3 (1) {}0,0),( ≠>= yxyx null S  S? { }0,00),( =>== yxxyx  ; {}0),( ≥= xyxS b (2) { }10),( 22 <+<= yxyx null S ; S? { }10),( 2222 =+=+= yxyxyx  ; { }1),( 22 ≤+= yxyxS b (3) ; = null S ? S? = ? ? ? ? ? ? ≤≤?==≤< 11,0 1 sin,10),( yx x yxyx  ; =S ? ? ? ? ? ? ≤≤?==≤< 11,0 1 sin,10),( yx x yxyx  b 2 5. p/ ?"￥ ?? ?  1 S = ? ? ? ? ? ? = + ? null,2,1 1 )1( k k k k   2 S = ? ? ? ? ? ? = ? ? ? ? ? ? null,2,1 5 2 sin, 5 2 cos k kk ππ   3 S = ? b )1)((|),{( 2222 +?+ xyyxyx }0 3 (1) b S' {}1±= (2) b S' =? (3) S' { }01),( 22 ≤+?= xyyx b 6. ￡ ü? ? 11.1.3 x ^?" S n R?  ￥ ?￥ sA1Hq ^ i  S?￥?  {x k }, ?@ x k ≠ x null,2,1=k   O x ∞→k lim k = x b ￡ A1? L ! x ^?" S￥ ? ? 1 k δ =   x￥ 1 k δ = #×? ? |B? x k ≠ x5μ x ∞→k lim k = x b  s?¨Q￡EbL ! x? ^?" S￥ ?5 x￥  #× (, ), 0O δ δ >x ? Koμ S￥μK?? ? [ (,) {}O δ ?∩S xx1μK" ? ^ inf{| | } 0d =?∈≠yx yS,y x> #?i S? ?@ x k ≠ x￥?  {x k } [ x1Ká 3 ±b 7. ! U ^ 2 R ￥ 7" ^? U￥ ???? ^ ?￥ ?b? 2 R ? ￥>"? ?? ;$ 3 7" U?￥ ??? xB? ^ ?￥ =? ?[ x￥ ?i #×?μ U ?￥íK?? ?[ xB? ^ U￥ ?b ?? S = ^{(0,0)} 2 R ￥>"7 SoμB?? ?[í ? '>"?￥??B? ^ ?￥ ?b 8. ￡ ü ￥ ?μ =?F?￥?" A ^ 7"b n RS ? null S ￡ L ! x 5∈S null 0δ?> (,)O δ ?xSb7 ? ∈y (,)O δx ?? (, | |) (,)OOδ δ?? ?yyx x ? [ y9 ^ S￥ =? V7 ? ^ A ^ 7"b o (,)O δ ?xS null S 9. ￡ ü ￥> n RS ? SSS ′= ∪ A ^>"b ￡ L ! x c ∈S  5 x?  O x? ^ S￥ ? ? ^ x￥  #×S (,)O δx ?àoμ S￥μK[#i x￥ #× 1 (, )O δx ?c S￥?' 3 1 (, )O δx c ? S V7 c S 1 7" ?[ SA ^>"b 10. ! b ? 1 7" F1>" ￡ ü 1 7" 1 >"b n RFE ?, E FE \ EF ￡ ?? 1>" ?[ 1 7" 7  9 ^ 7"b ? ? 1 7" ?[ 1>"V7 9 ^>"b F c F \EF c = EF∩ E c E c =FE F E∩ 11. ￡ ü Cantor> u×*? ?b ￡ L ! { ^d b>"?  ?@ } k S 12 1kk SS S S + ???? ?nullnull [# lim diam 0 k k S →∞ = b ? | k S k ∈x 5 ? m, n>k H V 7 ? ? , mn k S∈xx diam mn S?≤xx k k ? ^ { ^'?  V7 l ? ! K1 b ? ?i k? H } k x x mk≥ m S∈x  ?[ { ￥K} k x k SS k ∈ =x ? ^  ?[ d bb 1 k k S ∞ = ∈ ∩ x 1 k k S ∞ = ∩ ￡·B?bL ! 5 1 k k S ∞ = ∈ ∩ y diam k S?≤xy 0→    ?[ b k →∞ =xy 12.  è a ü ?@ 0lim 1 =? + ∞→ kk k xx ￥?  {x k }?B? l ?b 3 x k 1 1 k i i = =∈ ∑ R 5 1 1 lim lim 0 1 kk kk k + →∞ →∞ ? = + xx =7 |x k |= 1 1 k i i = →+∞ ∑  ?[ {x k }? l ?b 13. ! 1?"￡ ü ? 1?"b n RFE ?, FE∩ FE∪ ￡ y1 1?" ?[ 1μ?>" ? ^ V? ? 9? ^μ?>"'?"b n RFE ?, ,EF FE∩ FE∪ 4 14. ¨?l￡ ü?" ? ? ? ? ? ? = null∪ ,2,1 1 }0{ k k ^ R?￥?"b ￡ L? {}U α 1?" S= ? ? ? ? ? ? = null∪ ,2,1 1 }0{ k k ￥ ?B 7-?b ! 0 0 U α ∈  5 0 0: (0, )OU α δ δ?> ?  ? ^? 1 k δ > H 0 1 U k α ∈ b? 11 0,1, ,[ ]k k δ ? ? = ? ? ?? null  i {}U α ? k U α  P¤ 11 ,0,1,[ k Uk k α ] δ ∈=null b? ^ 0 1 ,0,1,[ k UU k αα ] δ ? = ? ?? null ? ? ? S￥μK 7-? ?[ S1?"b 15. ?¨ Heine-Borel? ?°¤￡ ü n R μ?íK?"Aμ ?b ￡ L? S1 n R μ?íK?"5?5 9 SSS ′= ∪ A ^>"b ?T Sí ?' 5 S1'=?S =SS' S1μ?>"V7? Heine-Borel? ?? S1 n R ￥?"b ?∈xS ?? x? ^ S￥ ? i (O )δ x x, ocμ S?μK??b A ? {( )| }O δ ∈ x x, x S ?1 S￥B? 7-? ??? ?μK? ()O δ x x, o ?c S?μK?? y7?i S￥μK 7-? ± ?[ S Aμ ?b 5