❇é ❣✐➳♦ ❞ơ❝ ✈➭ ➤➭♦ t➵♦ ❱✐Ư♥ ❦❤♦❛ ❤ä❝ ✫ ❝➠♥❣ ♥❣❤Ư ❱✐Ưt ◆❛♠ ❱✐Ư♥ ❚♦➳♥ ❤ä❝ ❚r➬♥ ➜×♥❤ ➜ø❝ ề t ị t ỉ ì ♥❤✐Ò✉ ❜✐Õ♥ ❈❤✉②➟♥ ♥❣➭♥❤✿ ●✐➯✐ tÝ❝❤ ▼➲ sè✿ ✻✷✳✹✻✳✵✶✳✵✶ ▲✉❐♥ ➳♥ ❚✐Õ♥ sÜ t♦➳♥ ❤ä❝ ❍➭ ◆é✐ ✷✵✶✶ ❇é ❣✐➳♦ ❞ơ❝ ✈➭ ➤➭♦ t➵♦ ❱✐Ư♥ ❦❤♦❛ ❤ä❝ ✫ ❝➠♥❣ ♥❣❤Ư ❱✐Ưt ◆❛♠ ❱✐Ư♥ ❚♦➳♥ ❤ä❝ ❚r➬♥ ➜×♥❤ ➜ø❝ ❱Ị t❐♣ ị t ỉ ì ề ế ❈❤✉②➟♥ ♥❣➭♥❤✿ ●✐➯✐ tÝ❝❤ ▼➲ sè✿ ✻✷✳✹✻✳✵✶✳✵✶ ▲✉❐♥ ➳♥ ❚✐Õ♥ sÜ t♦➳♥ ❤ä❝ ❚❐♣ t❤Ĩ ❤➢í♥❣ ❞➱♥ ❦❤♦❛ ❤ä❝ ●❙✳❚❙❑❍✳ ❍➭ ❍✉② ❑❤♦➳✐ ❚❙✳ ❱ò ❍♦➭✐ ❆♥ ❍➭ ◆é✐ ✷✵✶✶ ▲ê✐ ❝❛♠ ➤♦❛♥ ❚➠✐ ①✐♥ ❝❛♠ ➤♦❛♥ ➤➞② ❧➭ ❝➠♥❣ tr×♥❤ ♥❣❤✐➟♥ ❝ø✉ ❝đ❛ t➠✐ ❞➢í✐ sù ❤➢í♥❣ ❞➱♥ ❝đ❛ ●❙✳❚❙❑❍✳ ❍➭ ❍✉② ❑❤♦➳✐ ✈➭ ❚❙✳ ❱ò ❍♦➭✐ ❆♥✳ ❈➳❝ ❦Õt q✉➯ ✈✐Õt ❝❤✉♥❣ ➤➲ ➤➢ỵ❝ sù ♥❤✃t trÝ ❝đ❛ ➤å♥❣ t➳❝ ❣✐➯ ❦❤✐ ➤➢❛ ✈➭♦ ❧✉❐♥ ➳♥✳ ❈➳❝ ❦Õt q ợ trì tr tr tự từ ợ ố tr t ì ❝➠♥❣ tr×♥❤ ♥➭♦ ❦❤➳❝✳ ❚➳❝ ❣✐➯ ❚r➬♥ ➜×♥❤ ➜ø❝ ▼ơ❝ ❧ơ❝ ▼ë ➤➬✉ ❈❤➢➡♥❣ ✶ ✶✳✶ ✶✳✷ ✶✳✸ ✶ ➜Þ♥❤ ❧ý ❞✉② ♥❤✃t ❝❤♦ ❝➳❝ ➤➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ ♣❤ø❝ ▼ét sè ❦❤➳✐ ♥✐Ö♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ➜Þ♥❤ ❧ý ❞✉② ♥❤✃t ❝❤♦ ❝➳❝ ➤➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ ❦❤➳❝ ❤➺♥❣ ✳ ✶✷ ✳ ✶✸ ✳ ✶✾ ❚❐♣ ①➳❝ ➤Þ♥❤ ❞✉② ♥❤✃t ❝❤♦ ❝➳❝ ➤➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ ❦❤➠♥❣ s✉② ❜✐Õ♥ ➤➵✐ sè ❈❤➢➡♥❣ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ➜Þ♥❤ ❧ý ❞✉② ♥❤✃t ❝❤♦ ❝➳❝ ➤➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ ✷✳✶ ▼ét sè ❦❤➳✐ ♥✐Ư♠✳ ✷✳✷ ị ý t ỉ ì ❤➺♥❣✳ ✷✳✸ ✳ ✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ p ✳ ✳ ❈❤➢➡♥❣ ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ p✲❛❞✐❝ ✸✵ ✳ ✳ ✸✶ ✳ ✸✷ ✳ ✹✵ ✳ ✳ ✲❛❞✐❝ ❦❤➳❝ ✳ ✳ ❚❐♣ ①➳❝ ➤Þ♥❤ ❞✉② ♥❤✃t ❝❤♦ ❝➳❝ ➤➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ ❦❤➠♥❣ s✉② ❜✐Õ♥ ➤➵✐ sè✳ ✳ ✳ ✳ ✳ ✳ p ✳ ✳ ✳ ✳ ✲❛❞✐❝ ✳ ✳ ✳ ➜Þ♥❤ ❧ý ❞✉② ♥❤✃t ✈➭ ❜✐✲❯❘❙ ❝❤♦ ❝➳❝ ❤➭♠ ♣❤➞♥ ❤×♥❤ p✲❛❞✐❝ ♥❤✐Ị✉ ❜✐Õ♥ ✸✳✶ ✸✳✷ ✸✳✸ ▼ét sè ❦❤➳✐ ♥✐Ö♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ➜Þ♥❤ ❧ý ❞✉② ♥❤✃t ❝❤♦ ❝➳❝ ❤➭♠ ♣❤➞♥ ❤×♥❤ ➜❛ t❤ø❝ ❞✉② ♥❤✐Ị✉ ❜✐Õ♥ ✸✳✹ ✹✾ ♥❤✃t ✳ ✳ ✳ ✈➭ ✳ ✳ ❜✐✲❯❘❙ ✳ ✳ ✳ ✳ ✳ ❝❤♦ ✳ ✳ ❝➳❝ ✳ ✳ ✳ p ✳ ✳ ✳ ✳ ✳ ♣❤➞♥ ✳ ✳ ✳ ✳ p ❜✐Õ♥✳ ✳ ✳ ✳ ✳ ✳ ❑Õt ❧✉❐♥ ❝ñ❛ ❧✉❐♥ ➳♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ì ột ể ị ý í tứ ♣❤➞♥ ❤×♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✲❛❞✐❝ ♥❤✐Ị✉ ❜✐Õ♥✳ ❤➭♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ p ✳ ✳ ✺✵ ✳ ✺✺ ✳ ✻✶ ✳ ✻✹ ✲❛❞✐❝ ✳ ✳ ✳ ✲❛❞✐❝ ♥❤✐Ò✉ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✵ ❉❛♥❤ ♠ơ❝ ❝➳❝ ❝➠♥❣ tr×♥❤ ❧✐➟♥ q✉❛♥ ➤Õ♥ ❧✉❐♥ ➳♥ ✻✾ ❚➭✐ ❧✐Ö✉ t❤❛♠ ❦❤➯♦ ✼✵ ●✐➯✐ trì ề ệ sử ữ t ❝đ❛ ❝➳❝ ♣❤➯♥ ❜✐Ư♥ ✼✼ ✶ ▼ë ➤➬✉ ▼ét tr♦♥❣ ♥❤÷♥❣ ø♥❣ ❞ơ♥❣ s➞✉ s➽❝ ❝đ❛ ❧ý t❤✉②Õt ♣❤➞♥ ❜è ❣✐➳ trÞ ❞♦ ❘✳ ◆❡✈❛♥❧✐♥♥❛ ①➞② ❞ù♥❣ ❧➭ ❱✃♥ ➤Ị ị t ì ❤➺♥❣ tr➟♥ ♠➷t ♣❤➻♥❣ ♣❤ø❝ C q✉❛ ➤✐Ị✉ ❦✐Ư♥ ➯♥❤ ♥❣➢ỵ❝ ❝đ❛ t❐♣ ❤ỵ♣ ➤✐Ĩ♠✳ ◆➝♠ ✶✾✷✵✱ ●✳ Pã❧②❛ ❬✻✺❪ ❝❤ø♥❣ ♠✐♥❤ ➜Þ♥❤ ❧ý ✹ ➤✐Ĩ♠ s❛✉✿ ◆Õ✉ ❤❛✐ ❤➭♠ ♣❤➞♥ ❤×♥❤ ❦❤➳❝ ❤➺♥❣ f, g tr➟♥ ♠➷t ♣❤➻♥❣ ♣❤ø❝ C ❝ã ❝ï♥❣ ➯♥❤ ♥❣➢ỵ❝ ❦Ĩ ❝➯ ❜é✐ ❝đ❛ ✹ ➤✐Ĩ♠ ♣❤➞♥ ❜✐Ưt t❤× f = ♠➲♥ ad − bc = 0✳ ag + b ✈í✐ ♥❤÷♥❣ ❤➺♥❣ sè a, b, c, d ♥➭♦ ➤ã t❤♦➯ cg + d ◆➝♠ ✶✾✷✻✱ ❘✳ ◆❡✈❛♥❧✐♥♥❛ ➤➲ ❝❤ø♥❣ ♠✐♥❤✿ ◆Õ✉ ❤❛✐ ❤➭♠ ♣❤➞♥ ❤×♥❤ ❦❤➳❝ ❤➺♥❣ f, g tr➟♥ ♠➷t ♣❤➻♥❣ ♣❤ø❝ C ❝ã ❝ï♥❣ ➯♥❤ ♥❣➢ỵ❝ ❦❤➠♥❣ tÝ♥❤ ❜é✐ ❝đ❛ ✺ ➤✐Ĩ♠ ♣❤➞♥ ❜✐Ưt t❤× f ≡ g ◆❣➭② ♥❛②✱ ❦Õt q✉➯ ợ ọ ị ý ể ➤Õ♥ ♥❛②✱ ❝ã ❤❛✐ ❤➢í♥❣ ♥❣❤✐➟♥ ❝ø✉ s❛✉ ➤➞② ♥❤➺♠ ♠ë ré♥❣ ➜Þ♥❤ ❧ý ✹ ➤✐Ĩ♠✱ ➜Þ♥❤ ❧ý ✺ ➤✐Ĩ♠✳ ✶✮ ❳Ðt ♥❣❤Þ❝❤ ➯♥❤ r✐➟♥❣ rÏ ❝đ❛ ➤✐Ĩ♠ ❝❤♦ ❝➳❝ ❤➭♠ ✈➭ ♥❣❤Þ❝❤ ➯♥❤ ❝đ❛ s✐➟✉ ♣❤➻♥❣✱ s✐➟✉ ♠➷t ❝❤♦ ❝➳❝ ➳♥❤ ①➵ ❝❤Ø♥❤ ❤×♥❤✱ ✈í✐ ❝➳❝ t×♥❤ ❤✉è♥❣ ❦❤➠♥❣ tÝ♥❤ ❜é✐✱ p ❝ã tÝ♥❤ ❜é✐ ❤♦➷❝ tÝ♥❤ ✈í✐ ❜é✐ ị tr trờ ợ ứ ét ị ủ t ợ ể ị ủ t ợ s s t ❝❤♦ ❝➳❝ ➳♥❤ ①➵ ❝❤Ø♥❤ ❤×♥❤✱ ✈í✐ ❝➳❝ t×♥❤ ❤✉è♥❣ ❦❤➠♥❣ tÝ♥❤ ❜é✐✱ ❝ã tÝ♥❤ ❜é✐ ❤♦➷❝ tÝ♥❤ ✈í✐ ❜é✐ ị tr trờ ợ ứ p ❍➢í♥❣ t❤ø ♥❤✃t ❧➭ sù ♠ë ré♥❣ tù ♥❤✐➟♥ ❝đ❛ ➜Þ♥❤ ❧ý ✹ ➤✐Ĩ♠ ✈➭ ➜Þ♥❤ ❧ý ✺ ➤✐Ĩ♠✳ ❑Õt q✉➯ ➤➬✉ t✐➟♥ tr♦♥❣ tr➢ê♥❣ ❤ỵ♣ ♣❤ø❝ t❤✉é❝ ✈Ị ❍✳ ❋✉❥✐♠♦t♦ ❬✸✶❪✳ ◆➝♠ ✶✾✼✺✱ ➠♥❣ ❝❤ø♥❣ ♠✐♥❤ ➤➢ỵ❝✿ ◆Õ✉ ❤❛✐ ➳♥❤ ①➵ ♣❤➞♥ ❤×♥❤ ❦❤➳❝ ❤➺♥❣ f, g : Cm −→ Pn (C) ❝ã ❝ï♥❣ ➯♥❤ ♥❣➢ỵ❝ tÝ♥❤ ❝➯ ❜é✐ ❝đ❛ 3n + s✐➟✉ ♣❤➻♥❣ ✷ ë ✈Þ trÝ tỉ♥❣ q✉➳t tr♦♥❣ Pn (C) t❤× tå♥ t➵✐ ♠ét ❜✐Õ♥ ➤ỉ✐ t✉②Õ♥ tÝ♥❤ ①➵ ➯♥❤ L ❝đ❛ Pn (C) s❛♦ ❝❤♦ L(f ) = g ✳ ❚r♦♥❣ tr➢ê♥❣ ❤ỵ♣ p ✲❛❞✐❝ ❲✳ ❆❞❛♠s ✈➭ ❊✳ ❙tr❛✉s ❬✼❪ ➤➲ ♥❤❐♥ ➤➢ỵ❝ ❦Õt q✉➯ s❛✉ t➢➡♥❣ tù ♥❤➢ ➜Þ♥❤ ❧ý ✺ ➤✐Ĩ♠ ❝đ❛ ◆❡✈❛♥❧✐♥♥❛✿ ➜Þ♥❤ ❧ý ❆✳[7] ●✐➯ sư f, g ❧➭ ❤❛✐ ❤➭♠ ♣❤➞♥ ❤×♥❤ p✲❛❞✐❝ ❦❤➳❝ ❤➺♥❣ s❛♦ ❝❤♦ ➤è✐ ✈í✐ ✹ ❣✐➳ trÞ ♣❤➞♥ ❜✐Ưt a1 , a2 , a3 , a4 t❛ ❝ã f (z) = ❦❤✐ ✈➭ ❝❤Ø ❦❤✐ g(z) = , i = 1, 2, 3, 4✳ ❑❤✐ ➤ã f ≡ g P✳❈✳ ❍✉✲❈✳❈✳ ❨❛♥❣ ❬✸✾❪✱ ▼✳ ❘✉ ❬✺✹❪ ♠ë ré♥❣ ➜Þ♥❤ ❧ý A ❝❤♦ ❝➳❝ ➤➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ ❦❤➠♥❣ s✉② ❜✐Õ♥ t✉②Õ♥ tÝ♥❤✳ ❈➳❝ ➠♥❣ ➤➲ ❝❤ø♥❣ ♠✐♥❤✿ ➜Þ♥❤ ❧ý ❇✳ [39] ●✐➯ sö f, g : Cp −→ Pn (Cp ) ❧➭ ❤❛✐ ➤➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ ❦❤➠♥❣ s✉② ❜✐Õ♥ t✉②Õ♥ tÝ♥❤✱ Hi , 3n + ❧➭ ✸♥✰✶ s✐➟✉ ♣❤➻♥❣ i ë ✈Þ trÝ tỉ♥❣ q✉➳t tr♦♥❣ Pn (Cp ) t❤♦➯ ♠➲♥ f −1 (Hi ) f −1 (Hj ) = ∅ ✈í✐ ♠ä✐ i = j ✱ f −1 (Hi ) = g −1 (Hi ) ✈í✐ ♠ä✐ i = 1, , 3n + ✈➭ f (z) = g(z) ✈í✐ ♠ä✐ 3n+1 z∈ f −1 (Hi ) ❑❤✐ ➤ã f ≡ g i=1 ❚õ ➤ã✱ ❱✃♥ ➤Ò ị t t tứ t ợ ❝ø✉ ❧✐➟♥ tơ❝ ✈➭ ♠➵♥❤ ♠Ï ✈í✐ ❦Õt q✉➯ ❝đ❛ ❍✳ ❋✉❥✐♠♦t♦ ❬✸✷❪✱ ❬✸✸❪✱ ❬✸✹❪✱ ▼✳ ❘✉ ❬✺✹❪✱ ▲✳ ❙♠✐❧❡② ❬✺✾❪✱ ▼✳ ❙❤✐r♦s❛❦✐ ❬✺✼❪✱ ❚r❛♥ ❱❛♥ ❚❛♥ ❬ ✻✷❪✱ P✳ ❈✳ ❍✉ ✲ ❈✳ ❈✳ ❨❛♥❣ ❬✹✵❪✱ ●✳ ❉❡t❤❧♦❢❢ ✲ ❚✳❱✳ ❚❛♥ ❬✷✺❪✱ ❉✳❉✳ ❚❤❛✐ ✲ ❙✳ ❉✳ ◗✉❛♥❣ ❬✻✶❪✱ ❩✳ ❈❤❡♥ ✲ ❨✳ ▲✐ ✲ ◗✳ ❨❛♥ ❬✷✵❪✱ P✳ ❉✳ ❚❤♦❛♥ ✲ P✳ ❱✳ ❉✉❝ ✲ ❙✳ ❉✳ ◗✉❛♥❣ ❬✻✹❪✳✳✳ ❈❤♦ f ❧➭ ❤➭♠ ♣❤➞♥ ❤×♥❤ ❦❤➳❝ ❤➺♥❣ tr➟♥ Efm0 (S) = (z, m) ∈ C N : f (z) = a ① C ∪ {∞} ✈í✐ ❜é✐ n ✱ t❛ ➤Þ♥❤ ♥❣❤Ü❛ ✈➭ m= (m0 , n) ♠✐♥ a∈S ❚r♦♥❣ tr➢ê♥❣ ❤ỵ♣ m0 = ∞( t➢➡♥❣ ø♥❣ m0 = 1) ✱ ❝❤ó♥❣ t❛ ✈✐Õt Ef∞ (S) = Ef (S), ( t➢➡♥❣ ø♥❣ ❑ý ❤✐Ö✉✿ Pn (C) ❧➭ ❦❤➠♥❣ ❣✐❛♥ ①➵ ➯♥❤ ➜➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ f ❧➭ ➳♥❤ ①➵ n Ef1 (S) = E f (S)) ❝❤✐Ò✉ tr➟♥ tr➢ê♥❣ sè ♣❤ø❝ C ✳ f = [f1 : : fn+1 ] : C −→ Pn (C) ✸ ✈í✐ f1 , , fn+1 ❧➭ ❝➳❝ ❤➭♠ ♥❣✉②➟♥✱ ❦❤➠♥❣ f = (f1 , , fn+1 ) : C −→ Cn+1 − {0} ◆Õ✉ ✱ ✱ ë ➤ã ✱ t❤× ●✐➯ sư H f ➤✐Ĩ♠ ➳ ❝❤✉♥❣✳ ♥❤ fi = cgi c1 , , cn+1 ①➵ f ❧➭ ❤❛✐ ❜✐Ĩ✉ ❞✐Ơ♥ rót ❣ä♥ ❝đ❛ ❦❤➠♥❣ ❝ã ❦❤➠♥❣ ➤✐Ĩ♠ s❛♦ ❝❤♦ f (z) = [c1 : : cn+1 ] t❤ê✐ ❜➺♥❣ F = 0, c ❦❤➠♥❣ ❣ä✐ ❧➭ ♠ét ❜✐Ĩ✉ ❞✐Ơ♥ rót ❣ä♥ ❝đ❛ f = (f1 , , fn+1 ) g = (g1 , , gn+1 ) t❤× tå♥ t➵✐ ❤➭♠ ♥❣✉②➟♥ ◆Õ✉ ❝ã ✈í✐ ♠ä✐ ✳ f i ✱ ✳ ❧➭ ❝➳❝ ❤➺♥❣ sè ❦❤➠♥❣ ➤å♥❣ ➤➢ỵ❝ ❣ä✐ ❧➭ ➤➢ê♥❣ ❝♦♥❣ ❤➺♥❣✳ ❧➭ ♠ét s✐➟✉ ♣❤➻♥❣ ❝ñ❛ s ủ f Pn (C) ợ ị ❜ë✐ ♣❤➢➡♥❣ tr×♥❤ ❦❤➠♥❣ ❝❤ø❛ tr♦♥❣ H ✳ ➜➷t Ef (H) = EF◦ f (0), E f (H) = E F◦ f (0), k) = z ∈ C : F◦ f˜(z) = E f (H, , vF◦ f˜(z) k ❦❤➠♥❣ tÝ♥❤ ❜é✐ ❋✳ ●r♦ss ❬✸✼❪ ❧➭ ♥❣➢ê✐ ❦❤ë✐ ①➢í♥❣ ❤➢í♥❣ ♥❣❤✐➟♥ ❝ø✉ t❤ø ❤❛✐✳ ◆➝♠ ✶✾✼✼✱ ➠♥❣ ➤➢❛ r❛ ý t➢ë♥❣ ♠í✐ ❧➭ ❦❤➠♥❣ ①Ðt ➯♥❤ ♥❣➢ỵ❝ ❝đ❛ ❝➳❝ ➤✐Ĩ♠ r✐➟♥❣ rÏ ♠➭ ①Ðt ➯♥❤ ♥❣➢ỵ❝ ❝đ❛ ❝➳❝ t❐♣ ❤ỵ♣ ➤✐Ĩ♠ tr♦♥❣ C ∪ {∞} ✳ ↕♥❣ ➤➢❛ r❛ ❤❛✐ ❝➞✉ ❤á✐ s❛✉✿ ✶✮ ❚å♥ t➵✐ ❤❛② ❦❤➠♥❣ t❐♣ ❤×♥❤ f, g S t❤♦➯ ♠➲♥ ➤✐Ị✉ ❦✐Ư♥ ❝đ❛ ❚❐♣ S ❚➢➡♥❣ f, g s❛♦ ❝❤♦ ✈í✐ ❜✃t ❦ú ❝➳❝ ❤➭♠ ♣❤➞♥ Ef (S) = Eg (S), ✷✮ ❚å♥ t➵✐ ❤❛② ❦❤➠♥❣ ❤❛✐ t❐♣ ❤➭♠ ♣❤➞♥ ❤×♥❤ C ∪ {∞} {S1 , S2 } t❤♦➯ ♠➲♥ ➤✐Ị✉ ❦✐Ư♥ ❝đ❛ t❛ ❝ã f ≡g C ∪ {∞} ❄ s❛♦ ❝❤♦ ❜✃t ❦ú ❝➳❝ Ef (Si ) = Eg (Si ), i = 1, 2, t❤× f ≡g ❄ t❤♦➯ ♠➲♥ ✶✮ ❣ä✐ ❧➭ t❐♣ ①➳❝ ➤Þ♥❤ ❞✉② ♥❤✃t ✭✈✐Õt t➽t ❧➭ ❯❘❙✮✳ tù S1 , S2 t❤♦➯ ♠➲♥ ✷✮ ❣ä✐ ❧➭ s♦♥❣ ①➳❝ ➤Þ♥❤ ❞✉② ♥❤✃t ✭✈✐Õt t➽t ❧➭ ❜✐✲❯❘❙✮✳ ❑Õt q✉➯ ➤➬✉ t✐➟♥ t❤✉é❝ ✈Ò ❋✳ ●r♦ss ✈➭ ❈✳ ❈✳ ❨❛♥❣ ❬✸✽❪✳ ➠♥❣ ➤➲ ❝❤ø♥❣ ♠✐♥❤ t❐♣ S = {z ∈ C : z + ez = 0}, ◆➝♠ ✶✾✽✷✱ ❤❛✐ ❝ã ✈➠ ❤➵♥ ♣❤➬♥ tö✱ ❧➭ ❯❘❙ ❝❤♦ ❝➳❝ ❤➭♠ ♥❣✉②➟♥✳ ◆➝♠ ✶✾✾✹✱ ❍✳ ❳✳ ❨✐ ❧➬♥ ➤➬✉ t✐➟♥ ➤➢❛ r❛ ❯❘❙ ❤÷✉ ❤➵♥ ❝ã ✶✺ ♣❤➬♥ tư✳ ◆➝♠ ✶✾✾✽✱ ●✳ ❋r❛♥❦ ✈➭ ▼✳ ❘❡✐♥❞❡rs✱ ①➞② ❞ù♥❣ ❯❘❙ ❝ã ✶✶ ♣❤➬♥ tư✳ ➜è✐ ✈í✐ ❤➭♠ ♣❤➞♥ ❤×♥❤ p ✲❞✐❝✱ ♥➝♠ ✶✾✾✾✱ P✳❈✳ ❍✉✲❈✳ ❈✳ ❨❛♥❣ ❬✹✵❪ ①➞② ✹ ❞ù♥❣ ❯❘❙ ❝ã ✶✵ ♣❤➬♥ tư✳ ➜è✐ ✈í✐ ❊s❝❛ss✉t ❝➞✉ ❬✶✾❪ ❝❤Ø ({z1 , , zn }, w) ❞➵♥❣ ❤á✐ t❤ø r❛ ✈í✐ ❤❛✐ tå♥ t➵✐ ❝➳❝ ✳ ✈í✐ ♠ä✐ ❋✳ ❝➷♣ n ≥ ♠ä✐ ({z1 , , zn }, w) ❝ñ❛ ●r♦ss✱ ♥➝♠ ❜✐✲❯❘❙ ❝❤♦ ❈❤♦ n≥4 ➤Õ♥ ♥❛②✱ ✶✾✾✽✱ ❝➳❝ ❝➳❝ ❆✳ ❤➭♠ t❐♣ ❇♦✉t❛❜❛ ♣❤➞♥ ❜✐✲❯❘❙ ❤×♥❤ tèt ✲ ❆✳ ❞➵♥❣ ♥❤✃t ❧➭ t❤✉é❝ ✈Ị ❍➭ ❍✉② ❑❤♦➳✐✲❚➵ ❚❤Þ ❍♦➭✐ ❆♥ ❬✹✺❪✳ ❈❤♦ ➤Õ♥ ♥❛②✱ ➤➲ ❝ã ♥❤✐Ị✉ ❦Õt q✉➯ s➞✉ s➽❝ t❤❡♦ ❤➢í♥❣ t❤ø ❤❛✐ ♥❤➢ ❝ñ❛ ●✳ ❋r❛♥❦ ✲ ▼✳ ❘❡✐♥❞❡rs ❬✸✵❪✱ ❍✳ ❋✉❥✐♠♦t♦ ❬✸✹❪✱ ❈✳ ❈✳ ❨❛♥❣ ✲ ❳✳ ❍✉❛ ❬✻✼❪✱ ❍✳ ❳✳ ❨✐ ❬✻✽❪✱ ▼✉❡s ❊✳ ✲ ❘❡✐♥❞❡rs ▼✳ ❬✺✶❪✱ ❆✳ ❊s❝❛ss✉t ✲ ▲✳ ❍❛❞❞❛❞ ✲ ❘ ❱✐❞❛❧ ❬✷✽❪✱ ❍❛ ❍✉② ❑❤♦❛✐ ✲ ❚✳ ❚✳ ❍✳ ❆♥ ❬✹✹❪✱ ❬✹✺❪✱ ❲✳ ❈❤❡rr②✲ ❈✳ ❈✳ ❨❛♥❣ ❬✷✹❪✱ ❚❛ ❚❤✐ ❍♦❛✐ ❆♥ ❬✽❪✱ ❚✳ ❚✳ ❍✳ ❆♥ ✲ ❏✳❚✳❨✳❲❛♥❣ ✲ P✳▼✳❲♦♥❣ ❬✶✵❪✱ ❬✶✶❪✳✳✳ ❚❤❡♦ ❤❛✐ ❤➢í♥❣ ♥❣❤✐➟♥ ❝ø✉ ♥ã✐ tr➟♥✱ tr♦♥❣ ❧✉❐♥ ➳♥ ♥➭② ❝❤ó♥❣ t➠✐ ①Ðt ❝➳❝ ✈✃♥ ➤Ị s❛✉✿ ●✐➯ sư H1 , , Hq ❧➭ ❝➳❝ s✐➟✉ ♣❤➻♥❣ ë ✈Þ trÝ tỉ♥❣ q✉➳t tr♦♥❣ ❧➭ ❝➳❝ sè ♥❣✉②➟♥ ❞➢➡♥❣✳ ●ä✐ tõ C tí✐ Pn (C), f, g ∈ A, 1)E f (Hi , A Pn k1 , , kq ✱ ❧➭ t❐♣ ❝➳❝ ➤➢ê♥❣ ❝♦♥❣ ❝❤Ø♥❤ ❤×♥❤ ❦❤➳❝ ❤➺♥❣ t❤♦➯ ♠➲♥ ❝➳❝ ➤✐Ị✉ ❦✐Ư♥ s❛✉✿ ki ) = E g (Hi , ki ), q 2)f = g E f (Hi , tr➟♥ ki ) ✈í✐ ♠ä✐ i = 1, , q ✈➭ g ∈ A i=1 ❱✃♥ ➤Ị ✶✳ ❚×♠ ♠è✐ ệ ữ ề f g ì s ♠➷t X q ✈í✐ tr♦♥❣ ki ✈➭ Pn (C) n ➤Ó #A = s❛♦ ❝❤♦ ♥Õ✉ ✳ Ef (X) = Eg (X) t❤× ✳ ❱✃♥ ➤Ị ✸✳ ✸✳✶✳ ✸✳✷✳ ❚➢➡♥❣ tù ❱✃♥ ➤Ò ✶ ✈➭ ❱✃♥ ➤Ò ✷ tr♦♥❣ trờ ợ tự ị ý ể trờ ợ p p ✲❛❞✐❝✳ ➜Þ♥❤ ❧ý ✺ ➤✐Ĩ♠ ✈➭ t❤✐Õt ❧❐♣ ❜✐✲❯❘❙ ❝❤♦ ✲❛❞✐❝ ♥❤✐Ò✉ ❜✐Õ♥✳ ❚r♦♥❣ ❝➳❝ ✈✃♥ ➤Ò tr➟♥✱ ♥Õ✉ sè q ✈➭ ❜❐❝ ❝ñ❛ s✐➟✉ ♠➷t ❝➭♥❣ ♥❤á✱ ị s t rộ tì ết q tì ợ ó ý ĩ ố ♠ô❝ t✐➟✉ ❞✐ ➤é♥❣ ✈➭ f, g : Cm −→ Pn (C) ❧➭ ➳♥❤ ①➵ ♣❤➞♥ ❤×♥❤ q ❦❤➳❝ ❤➺♥❣✿ ●✐➯ sư {ai }i=1 ❧➭ ❝➳❝ ➳♥❤ ①➵ ♣❤➞♥ ❤×♥❤ tõ Cm ✈➭♦ Pn (C) ë ✈Þ trÝ tỉ♥❣ q✉➳t s❛♦ ❝❤♦ ❧➭ ♥❤á ➤è✐ ✈í✐ f ✱ (f, ) ≡ 0, i = 1, , q ✈➭ t❤♦➯ ♠➲♥✿ a) ❞✐♠{z ∈ Cm |(f, )(z) = (f, aj )(z) = 0} b) ♠✐♥(v(f,aj ) , d) = ♠✐♥(v(g,aj ) , d), j m − (1 i