[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む13 [転載禁止]©2ch.net (654ﾚｽ)
上下前次1-新
抽出解除 ﾚｽ栞

---

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索 歴削→次ｽﾚ 栞削→次ｽﾚ 過去ﾛｸﾞﾒﾆｭｰ

---

258(3): 現代数学の系譜11 ガロア理論を読む 2015/05/01(金)04:22 ID:kLen/OPb(2/7) AAS
>>257 つづき

外部ﾘﾝｸ[pdf]:www.maa.org
MATHEMATICS MAGAZINE 1966
AUTOMORPHISMS OF THE COMPLEX NUMBERS
PAUL B. YALE，Pomona College

　 One of the best known bits of mathematical folklore is that there are many automorphisms of the field of complex numbers，
i.e .，that the complex numbers can be permuted in many ways (besides the familiar complex conjugation) that preserve addition and multiplication.
省6

---

259(2): 現代数学の系譜11 ガロア理論を読む 2015/05/01(金)05:03 ID:kLen/OPb(3/7) AAS
>>258 つづき

THEOREM 4. If φ is a wild automorphism of C then φ is a discontinuous mapping of the complex plane onto itself;
in fact，φ leaves a dense subset of the real line pointwise fixed but maps the real line onto a dense subset of the plane.

Proof. By Theorem 2，φ leaves Q (a dense subset of the real line!) pointwise fixed.
By Theorem 3 we can choose b∈R such that φ(b) not∈R.
Every neighborhood of b contains a rational number (which is left fixed by φ) and the number b (which is moved by φ); hence φ is discontinuous.
For every pair of rational numbers， q and r，φ(rb+q) =φ(r)φ(b)+φ(q)=rφ(b) +q.
省5

---

285(3): 現代数学の系譜11 ガロア理論を読む 2015/05/04(月)21:19 ID:jADohwWI(4/10) AAS
>>283　訂正

おっちゃんの主題のおかけで
　↓
おっちゃんの出題のおかけで

（本題）
そういえば、>>258 外部ﾘﾝｸ[pdf]:www.maa.org
MATHEMATICS MAGAZINE 1966
省12

---

335(2): 現代数学の系譜11 ガロア理論を読む 2015/05/06(水)09:47 ID:SXg2oFIb(7/21) AAS
>>328 つづき

おっちゃんのために
PAUL B. YALE，Pomona College >>258 より

P137
THEOREM 2. Any isomorphism between sub fields of C extends IQ, the identity map on Q.

THEOREM 3. The only isomorphisms between sub fields of C whose domains include R and which map R into R are IR, Ic, and complex conjugation.

Proof. Let Φ be such an isomorphism, i.e., assume R⊆domain Φ and x∈R
省16

---

上下前次1-新書関写板覧索設栞歴

---

ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ

---

ぬこの手 ぬこTOP 0.044s