❇❐ ●■⑩❖ ❉Ư❈ ❱⑨ ✣⑨❖ ❚❸❖ ❚❘×❮◆● ✣❸■ ❍➴❈ ◗❯❨ ◆❍❒◆ ✯✯✯✯✯✯✯✯✯ ❍⑨ ❉❯❨ ◆●❍➒❆ ❚➷P➷ ❚❍×❒◆● ✣➮■ ❱❰■ ▼❐❚ ⑩◆❍ ❳❸ ❚■➎❯ ▲❯❾◆ ❚➷P➷ ✣❸■ ❙➮ ◗✉② ◆❤ì♥✱ t❤→♥❣ ✹ ♥➠♠ ✷✵✶✵ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❇❐ ●■⑩❖ ❉Ư❈ ❱⑨ ✣⑨❖ ❚❸❖ ❚❘×❮◆● ✣❸■ ❍➴❈ ◗❯❨ ◆❍❒◆ ✯✯✯✯✯✯✯✯✯ ❍⑨ ❉❯❨ ◆●❍➒❆ ❚➷P➷ ❚❍×❒◆● ✣➮■ ❱❰■ ▼❐❚ ⑩◆❍ ❳❸ ❈❆❖ ❍➴❈ ❚❖⑩◆ ❑❍➶❆ ✶✶ ❈❤✉②➯♥ ♥❣➔♥❤✿ số ỵ tt số P ữớ ữợ P ◆❤ì♥✱ t❤→♥❣ ✹ ♥➠♠ ✷✵✶✵ ✐ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ▼Ư❈ ▲Ư❈ ❚r❛♥❣ ♣❤ư ❜➻❛ ✐ ▼ư❝ ❧ư❝ ✶ ▲í✐ ♠ð ✤➛✉ ✷ ✶ ❈→❝ ❦❤→✐ ♥✐➺♠ ✈➔ t➼♥❤ ❝❤➜t ❝õ❛ tỉ♣ỉ t❤÷ì♥❣ ✸ ✷ ❇➔✐ t➟♣ ✺ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ✾ ✶ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ▲❮■ ▼Ð ✣❺❯ ❚æ♣æ ✤↕✐ sè ❧➔ ♠ët ❜ë ♠ỉ♥ t♦→♥ ❤å❝ ♠ỵ✐ ♠➫ ✈➔ ❝ü❝ ❦ý q✉❛♥ trå♥❣✱ ♥❣÷í✐ t❛ ❞ị♥❣ ❝ỉ♥❣ ❝ư ✤↕✐ sè ✤➸ ♥❣❤✐➯♥ ❝ù✉ ❝➜✉ tró❝ ❝→❝ ❦❤ỉ♥❣ ❣✐❛♥ tỉ♣ỉ ✳ ❈â ♥❤✐➲✉ ❦➳t q✉↔ t❤ó ✈à ♥❤÷ ❞ị♥❣ ổ tổổ số ự ỵ t rr ỵ ỡ sè✱ ✤➦❝ ❜✐➺t ❦➳t q✉↔ ♥ê✐ t✐➳♥❣ ♥❤➜t ✤â ❧➔ ❣✐↔ t❤✐➳t P♦✐♥❝❛r➨✱✳✳ ❚r♦♥❣ ❦❤✉ỉ♥ ❦❤ê t✐➸✉ ❧✉➟♥ ❦➳t t❤ó❝ ❜ë ♠æ♥✱ tæ✐ ①✐♥ tr➻♥❤ ❜➔② ♠ët sè ✈➜♥ ✤➲ q tổổ tữỡ ố ợ ởt t ỗ ũ ợ ✤➛✉✱ ❦➳t ❧✉➟♥ ✈➔ t➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦✿ ✶✳ ❑❤æ♥❣ tổổ tữỡ ố ợ ởt ❞ư♥❣ ❝❤ù♥❣ ♠✐♥❤ ❤❛✐ ❦❤ỉ♥❣ ❣✐❛♥ CP ✈➔ S ỗ ổ ũ t rt ố tr t ự ữủ sỹ ữợ t t t ữợ ữ ♥➠♥❣ ❧ü❝ ❝õ❛ ❜↔♥ t❤➙♥ ✈➔ t❤í✐ ❣✐❛♥ ❝á♥ ❤↕♥ ❝❤➳ ♥➯♥ t✐➸✉ ❧✉➟♥ ❦❤â tr→♥❤ ❦❤ä✐ ♥❤ú♥❣ t❤✐➳✉ sât✳ ổ rt ữủ sỹ õ ỵ qỵ t❤➛② ❝ỉ ✈➔ ❝→❝ ❜↕♥ ✤➸ t✐➸✉ ❧✉➟♥ ✤÷đ❝ ❤♦➔♥ t❤✐➺♥ ❤ì♥✳ ❈✉è✐ ❝ị♥❣ tỉ✐ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥ P●❙✳❚❙ ◆❣✉②➵♥ ❙✉♠ ♥❣÷í✐ ✤➣ t➟♥ t➻♥❤ ❣✐↔♥❣ ❞↕②✱ ❣✐ó♣ ✤ï✱ ❝ị♥❣ t➟♣ t❤➸ ❧ỵ♣ ❝❛♦ ❤å❝ t♦→♥ ❦❤♦→ ✶✶ t↕♦ ✤✐➲✉ ❦✐➺♥ ❝❤♦ tæ✐ ❤♦➔♥ t❤➔♥❤ t✐➸✉ ❧✉➟♥ ♥➔②✳ ✷ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❚æ♣æ tữỡ ố ợ ởt r ❑❍⑩■ ◆■➏▼ ❱⑨ ❚➑◆❍ ❈❍❻❚ ❈Õ❆ ❚➷P➷ ❚❍×❒◆● ✣à♥❤ ♥❣❤➽❛ ✶✳✶✳ ❈❤♦ X ❧➔ ❦❤æ♥❣ ❣✐❛♥ tæ♣æ ✱ Y ❧➔ t➟♣ ❤ñ♣ ❦❤→❝ ré♥❣✱ →♥❤ ①↕ f : X −→ Y ❧➔ t♦➔♥ →♥❤ ❧✐➯♥ tö❝✱ ❣å✐ ❯f = {U ⊂ Y, f −1(U ) ♠ð tr♦♥❣X} ❦❤✐ ✤â ❯f tổổ tr Y tổổ tữỡ ố ợ f ✳ ❚❤➟t ✈➟②✿ ♠ð tr♦♥❣ X ✈➟② Ø ∈ ❯f f −1 (Y ) = X − ♠ð ⇒ Y ∈ ❯f ✳ • Ø = f −1 (Ø) • • U1 , U2 ∈ ❯f , f −1 (U1 ∩ U2 ) = f −1 (U1 ) ∩ f −1 (U2 ) • {Ui , i ∈ I} ⊂ ❯f ⇒ f −1 (Ui ) ♠ð ∀i ∈ I ✱ f −1 ♠ð✱ s✉② r❛ Ui ∈ ❯f i∈I ✣✐➲✉ ♥➔② ❝❤ù♥❣ tä ❯f ❧➔ tæ♣æ tr➯♥ Y ✳ ✲♠ð ⇒ U1 ∩ U2 ∈ ❯f ✳ Ui i∈I f −1 (Ui ) = i∈I ❧➔ ❱➼ ❞ö ✶✳✷✳ ❑❤æ♥❣ ❣✐❛♥ ①↕ ↔♥❤ t❤ü❝ RP n = {❈→❝ ❦❤æ♥❣ ❣✐❛♥ ❝♦♥ ✶ ❝❤✐➲✉ ❝õ❛ Rn+1.} ❳➨t ♣❤➨♣ ❝❤✐➳✉ p : Rn+1\{0} −→ RP n, p(x) = [x] = αx, α ∈ R ✱ ❧➔ t♦➔♥ →♥❤✱ ♥➯♥ t❛ õ RP n ổ tổổ ợ tổổ tữỡ ố ợ p ã ổ ♣❤ù❝ RP n = {❈→❝ ❦❤æ♥❣ ❣✐❛♥ ❝♦♥ ✶ ❝❤✐➲✉ ❝õ❛ Cn+1 }✳ ❚÷ì♥❣ tü✱ ①➨t ♣❤➨♣ ❝❤✐➳✉ q : Cn+1\{0} −→ CP n, q(x) = [x] = {αx, α ∈ R} ❧➔ t♦➔♥ →♥❤ ✈➔ t❛ ❝ô♥❣ ❝â CP n ổ tổ ợ tổổ tữỡ ố ợ q✳ • ❈❤♦ X ❧➔ ❦❤ỉ♥❣ ❣✐❛♥ tỉ♣ỉ ∼ ❧➔ q✉❛♥ ❤➺ t÷ì♥❣ ✤÷ì♥❣ tr➯♥ X ✱ ✤➦t Y = X t tữỡ ỗ tt ợ t÷ì♥❣ ✤÷ì♥❣ ❝õ❛ x ∈ X ✱ ❦❤✐ ✤â Y ổ tổổ ợ tổổ tữỡ ố ợ p : X Y ã ỵ ✶✳✸✳ ❈❤♦ X, Z ❧➔ ❤❛✐ ❦❤æ♥❣ ❣✐❛♥ tæ♣æ ✱ Y ❧➔ t➟♣ ❤ñ♣✱ f : X −→ Y ❧➔ t♦➔♥ ❝➜✉✱ ❣✐↔ sû r➡♥❣ Y ❧➔ ❦❤æ♥❣ ❣✐❛♥ tæ♣æ ợ tổổ tữỡ ố ợ f õ g : Y −→ Z ❧✐➯♥ tö❝ ❦❤✐ ✈➔ ❝❤➾ ❦❤✐ g ◦ f : X −→ Z ❧✐➯♥ tö❝✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❚ỉ♣ỉ t❤÷ì♥❣ ✤è✐ ✈ỵ✐ ♠ët →♥❤ ①↕ ❚r❛♥❣ ✹ ❈❤ù♥❣ ♠✐♥❤✳ (⇒)✳ tt Y tổổ ợ tổổ tữỡ ✈ỵ✐ →♥❤ ①↕ f ♥➯♥ ✈ỵ✐ U ❧➔ t➟♣ ♠ð tr♦♥❣ Y t❛ ❝â f −1(U ) ❧➔ ♠ð tr♦♥❣ X ♥➯♥ f ❧➔ →♥❤ ①↕ ❧✐➯♥ tö❝✳ ◆❣♦➔✐ r❛ t❛ ❝â g ❧✐➯♥ tö❝ ♥➯♥ g ◦ f ❧✐➯♥ tư❝✳ ◆❣÷đ❝ ❧↕✐✱ ❣✐↔ sû g ◦ f ❧✐➯♥ tư❝✱ ✈ỵ✐ ♠å✐ V ♠ð tr♦♥❣ Z t❛ ❝â ✿(g ◦ f )−1(V ) ♠ð tr♦♥❣ X ✱♥➯♥ (g ◦ f )−1(V ) = f −1(g−1(V )) ♠ð tr♦♥❣ Y ✱ s✉② r❛ g−1(V ) ∈ ❯f ) ❞♦ ✤â g−1(V ) ♠ð tr♦♥❣ Y ✳ ❱➟② g ❧✐➯♥ tö❝✳ ◆❤➟♥ ①➨t ✶✳✹✳ ❚ỉ♣ỉ t❤÷ì♥❣ σ tr➯♥ t➟♣ t❤÷ì♥❣ X/ ∼ ❧➔ tæ♣æ ♠↕♥❤ ♥❤➜t ❧➔♠ ❝❤♦ →♥❤ ①↕ ❝❤➼♥❤ t➢❝ f ❧✐➯♥ tö❝✳ ❚❤➟t ✈➟②✱ ❣✐↔ sû tr➯♥ X/ ∼ ❧➔♠ ❝❤♦ →♥❤ ①↕ ❝❤➼♥❤ t➢❝ f ❧✐➯♥ tö❝✳ ❑❤✐ ✤â ❜➜t ❦ý G t❤✉ë❝ t❤➻ f −1(G)❧➔ t➟♣ ♠ð tr♦♥❣ X ✱ ❞♦ ✤â t❤❡♦ ✤à♥❤ ♥❣❤➽❛ tỉ♣ỉ t❤÷ì♥❣ t❤➻ G ∈ σ✱ ✈➟② ≤ σ✳ ▼➺♥❤ ✤➲ ✶✳✺✳ ❈❤♦ X ❧➔ G✲❑❤æ♥❣ ❣✐❛♥ ✭X ❧➔ ❦❤æ♥❣ ❣✐❛♥ tæ♣æ ✱ G ❧➔ ♥❤â♠ tæ♣æ ✮ ❦❤✐ ✤â ♣❤➨♣ ❝❤✐➳✉ π : X −→ X/G, π(x) = Gx ❧➔ →♥❤ ①↕ ♠ð✳ ❈❤ù♥❣ ♠✐♥❤✳ ∀U ⊂ X ❧➔ t➟♣ ♠ð✱ t❛ ❝â ✿ π −1 (π(U )) = {x ∈ X | π(x) ∈ π(U )} = {x ∈ X | ∃y ∈ U : π(x) = π(y)} = {x ∈ X | ∃g ∈ G, y ∈ Y : x = gy} = {x ∪ gU g∈G ❚ø θg : X X, (x) = gx ỗ ♣❤æ✐ ✈➔ U ♠ð tr♦♥❣ X ♥➯♥ gU tr♦♥❣ X ✳ ❉♦ ✤â ∪ gU ♠ð tr♦♥❣ X ✱ ✈➟② π(U ) ❧➔ ♠ð✱ ❤❛② π ❧➔ →♥❤ ①↕ ♠ð✳ gG ỵ X ổ t ❍❛✉s❞♦r❢❢ t❤➻ ✿ i)◆➳✉ G ❧➔ ♥❤â♠ ❤ú✉ ❤↕♥ ✈➔ X ❧➔ G✲❦❤æ♥❣ ❣✐❛♥✱ t❤➻ X/G ❧➔ ❦❤æ♥❣ ❣✐❛♥ ❝♦♠♣❛❝t ❍❛✉s❞♦r❢❢✳ ii)◆➳✉ A ❧➔ ❦❤æ♥❣ ❣✐❛♥ ❝♦♥ ✤â♥❣ ❝õ❛ X ✱ t❤➻ X/A ❧➔ ❝♦♠♣❛❝t ❍❛✉s❞♦r❢❢✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ổổ tữỡ ố ợ ởt ①↕ ❚r❛♥❣ ✺ ✷ ❇⑨■ ❚❾P ⑩P ❉Ö◆● ❇➔✐ t♦→♥✿ r➡♥❣ ✿ ✶✳ ✷✳ ●å✐ S n = {∈ Rn+1| x = 1} ❧➔ ♠➦t ❝➛✉ n ❝❤✐➲✉✱ ❝❤ù♥❣ ♠✐♥❤ RP ∼ = S1 CP ∼ = S P ự t t ữợ s ữợ t ỹ t tữỡ X/A, A ⊂ X ✳ ❈❤♦ X ❧➔ ❦❤æ♥❣ ❣✐❛♥ tæ♣æ ✱ A ⊂ X ✤à♥❤ ♥❣❤➽❛ q✉❛♥ ❤➺ t÷ì♥❣ ✤÷ì♥❣ tr➯♥ X ♥❤÷ s❛✉✿ ∀x, y ∈ X, x ∼ y ⇔ x=y x, y ∈ A ❉➵ ❦✐➸♠ tr❛ ✤÷đ❝ ∼ ❧➔q✉❛♥ ❤➺ t÷ì♥❣ ✤÷ì♥❣ tr➯♥ X ✱ ❑❤✐ ✤â✿ ∀x ∈ X, [x] = ❙✉② r❛ ✿ {x}, x ∈ A A, x ∈ A X/ ∼= (X \ A) {A} = X/A ữợ ự ♠✐♥❤ S+1 /A ∼ = S ✣➦t X = S+1 = {(x, y) ∈ R2, x2 + y2 = 1, y ≥ 0}., A = {(−1, 0), (1, 0)} ❳➨t →♥❤ ①↕ f : S −→ S+1 /A, f (x) = [x] t ự f ỗ ổ ✳ • f ❧✐➯♥ tư❝ ✈➔ t♦➔♥ →♥❤ ❧➔ ❤✐➸♥ ♥❤✐➯♥ • ❈❤ù♥❣ ♠✐♥❤ ❢ ✤ì♥ →♥❤ ∀(x1 , y1 ), (x2 , y2 ) ∈ S ✱ ❣✐↔ sû f (x1 , y1 ) = f (x2 , y2 ) ⇔ [(x1 , y1 )] = [(x2 , y2 )] ✤✐➲✉ ♥➔② s✉② r❛✿ (x1, y1) = (x2, y2) ❤♦➦❝ (x1, y1), (x2, y2) ∈ A ◆➳✉ (x1, y1) = (x2, y2) t❤➻ f ✤ì♥ →♥❤ ❧➔ ✤ó♥❣✳ ◆➳✉ (x1, y1), (x2, y2) ∈ At❤➻ [(x1, y1)] = [(x2, y2)] = A ✤✐➲✉ ♥➔② ❝ô♥❣ ❝❤ù♥❣ tä (x1 , y1 ) = (x2 , y2 )✳ ❱➟② f ❧➔ ✤ì♥ →♥❤ ◆❣♦➔✐ r❛✱ S ❧➔ ❍❛✉s❞♦❢❢✱ S+1 /A t f ỗ ổ S+1 /A ∼ = S LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ổổ tữỡ ố ợ ởt r ữợ ự RP = S t sỡ ỗ s S+1 F FF FF f FF FF F# g / S /A p RP + ❚r♦♥❣ ✤â p ❧➔ ♣❤➨♣ ❝❤✐➳✉ ❧➔ t♦➔♥ →♥❤ ❝❤➼♥❤ t➢❝✱ ❝á♥ f ✤÷đ❝ ①→❝ ✤à♥❤ ♥❤÷ s❛✉ f (x, y) = [x : y] = {α(x, y), α ∈ R}✱ ❞➵ ❝❤ù♥❣ ♠✐♥❤ ✤÷đ❝ f ❝ơ♥❣ ❧➔ t♦➔♥ →♥❤✳ ❇➙② ❣✐í t❛ ①→❝ ✤à♥❤ g ♥❤÷ s❛✉✿g[(x, y)] = [x : y]✳ ❑❤✐ ✤â ∀(x, y) ∈ R2, g(p(x, y)) = g[(x, y)] = α(x, y) = f (x, y)✱ ✈➟② g ◦ p = f ◆❣♦➔✐ r❛✱ f ❧➔ t♦➔♥ →♥❤ ♥➯♥ g ❝ơ♥❣ t♦➔♥ →♥❤✱ t❛ ❝➛♥ ❝❤ù♥❣ ♠✐♥❤ g ✤ì♥ →♥❤✿ ∀[(x1 , y1 )], [(x2 , y2 )] ∈ S+1 /A ✱ ❣✐↔ sû g[(x1 , y1 )] = g[(x2 , y2 )] ⇔ [(x1 : y1 ] = [x2 , y2 ] ⇔ (x , y1 ) = α(x2 , y2 ), α ∈ R x1 = αx2 ⇒ y1 = αy2 ◆➳✉ α = 1t❤➻ [(x1, y1)] = [(x2, y2)] ❧➔ ✤ó♥❣✳ ◆➳✉ α = t❛ ❝â α2(x22 + y22) = x21 + y12 = ⇒ α = −1 x1 = −x2 ❦❤✐ ✤â ❉♦ y1 = −y2 y2 ≥ ♥➯♥ y2 = ⇒ x2 = [(x1 , y1 )] = [(x2 , y2 )] s✉② r❛ g ✤ì♥ →♥❤✳ tø ✤â s✉② r❛ (x1 , y1 ), (x2 , y2 ) ∈ A ❤❛② ▼➦t ❦❤→❝ t❛ ❝â ✿ f ❧✐➯♥ tö❝✱ p ❧✐➯♥ tö❝ ♥➯♥ g ❧✐➯♥ tö❝✳ RP ❧➔ ❍❛✉s❞♦r❢❢✱ S+1 /A ❧➔ t s r g ỗ ổ RP ∼ = S 1✳ ❚÷ì♥❣ tü ♥❤÷ tr➯♥✱ ✤➦t X = S+2 = {(x, y, z) ∈ R3 , x2 + y + z = 1, z ≥ 0}, S+1 = {(x, y, 0) ∈ R3 , x2 + y = 1} ❚❛ ❝❤ù♥❣ CP = S ữ s rữợ ❤➳t ❝❤ù♥❣ ♠✐♥❤ S ∼ = S+2 /S+1 ❳➨t →♥❤ ①↕ f : S −→ S+2 /S+1 ✱ ❢✭①✱②✱③✮❂❬✭①✱②✱③✮❪ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❚æ♣æ tữỡ ố ợ ởt r f ❧✐➯♥ tö❝ ✈➔ t♦➔♥ →♥❤ ❚❛ ❝➛♥ ❝❤ù♥❣ ♠✐♥❤ f ✤ì♥ →♥❤✿ ∀(x1 , y1 , z1 ), (x2 , y2 , z2 ) ∈ S , ❣✐↔ sû f (x1 , y1 , z1 ) = f (x2 , y2 , z2 ) ⇔ [(x1 , y1 , z1 )] = [(x2 , y2 , z2 )] ❤♦➦❝ (x1, y1, z1), (x2, y2, z2) ∈ S+1 ◆➳✉ (x1, y1, z1) = (x2, y2, z2) t❤➻ f ✤ì♥ →♥❤ ❧➔ ✤ó♥❣✳ ◆➳✉ (x1, y1, z1), (x2, y2, z2) ∈ At❤➻ [(x1, y1, z1)] = [(x2, y2, z2)] ❝ô♥❣ ❝❤ù♥❣ tä (x1, y1, z1) = (x2, y2, z2)✳ ❱➟② f ❧➔ ✤ì♥ →♥❤✳ ❱➟② S+2 /S+1 ∼ = S (x1 , y1 , z1 ) = (x2 , y2 , z2 ) = A ữợ ❈❤ù♥❣ ♠✐♥❤ CP ∼ = S t❤❡♦ ỗ S+2 QQQ QQQ QQQf QQQ QQQ QQ( g / S /S p S2 ∼ = + + [(x, y, z)] / CP (x + iy : z) ❚r♦♥❣ ✤â →♥❤ ①↕ f ✤÷đ❝ ①➙② ❞ü♥❣ ♥❤÷ s❛✉✿ / f : S+2 (x, y, z) / CP (x + iy : z) ❞➵ ❝❤ù♥❣ ♠✐♥❤ ✤÷đ❝ ❢ ❧✐➯♥ tư❝ ✈➔ t♦➔♥ →♥❤✱ ❦❤✐ ✤â ❣å✐ / g : S+2 /S+1 [(x, y, z) / CP [x + iy : z] t❛ ❝â ✤÷đ❝ f = g ◦ p ✈➔ ❞♦ f ❧➔ t♦➔♥ →♥❤ ♥➯♥ g ❝ô♥❣ t♦➔♥ →♥❤✳ ❚❛ ❝➛♥ ❝❤ù♥❣ ♠✐♥❤ g ✤ì♥ →♥❤ ∀[(x1 , y1 z1 , )], [(x2 , y2 , z2 )] ∈ S+2 /S+1 ✱ ❣✐↔ sû g[(x1 , y1 , z1 )] = g[(x2 , y2 , z2 )] ⇔ [x1 + iy1 : z1 ] = [x2 + iy2 : z2 ] LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❚ỉ♣ỉ t❤÷ì♥❣ ✤è✐ ✈ỵ✐ ♠ët →♥❤ ①↕ ❚r❛♥❣ ✽ ⇔ (x1 + iy1 )z2 = (x2 + iy2 )z1 ) ⇔ (x21 + y12 )z22 = (x22 + iy2 z12 ⇒ (1 − z12 )z22 = (1 − z22 )z12 ⇒ z2 = z1 ◆➳✉ z1 = z2 = t❤➻ (x1, y1z1, ), (x2, y2, z2) ∈ S+1 ❞♦ ✤â [(x1, y1z1, )] = [(x2, y2, z2)] ◆➳✉ z1 = z2 > t❤➻ x1 = x2, y1 = y2 ❞♦ ✤â [(x1, y1z1)] = [(x2, y2, z2)] ✣✐➲✉ ♥➔② ❝❤ù♥❣ tä g ✤ì♥ →♥❤✳ ◆❣♦➔✐ r❛ f ✱ ❧✐➯♥ tư❝✱p ❧✐➯♥ tư❝ ♥➯♥ g ❝ơ♥❣ ❧✐➯♥ tư❝ ✈➔ S+2 /S+1 ❧➔ ❝♦♠♣❛❝t ✱CP ❧➔ ❍❛✉s❞♦r❢❢ ♥➯♥ t❛ s✉② r❛ ữủ g ỗ ổ CP = S LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ổổ tữỡ ố ợ ởt r ❚➔✐ ❧✐➺✉ ✶✳ ❚➔✐ ❧✐➺✉ ❤å❝ t➟♣ ❚æ♣æ ✤↕✐ sè ❈❛♦ ❤å❝ t♦→♥ ❦❤â❛ ✶✶✳ ✷✳ ❏✐❡ ❲✉✳ ▲❡❝t✉r❡ ◆♦t❡s ♦♥ ❆❧❣❡❜r❛✐❝ ❚♦♣♦❧♦❣② ✱◆❛t✐♦♥❛❧ ❯♥✐✈❡rs✐t② ♦❢ ❙✐♥❣❛✲ ♣♦r❡✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com