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数学 大学生・専門学校生・社会人

多様体を構成するために、位相空間に完全アトラスを導入するところで質問です。 完全アトラスを導入するメリットとして、この文章の下線部を「異なる座標系を用いたのに同じ計算ができてしまうという問題が解消される」解釈したのですが、そこがよくわかりません。座標系を変えて計算する... 続きを読む

1 Two n-dimensional coordinate systems & and ŋ in S overlap smoothly provided the functions on¯¹ and ŋo §¯¹ are both smooth. Explicitly, if : U → R" and ŋ: R", then ŋ 1 is defined on the open set ε (ur) → ° (UV) V and carries it to n(u)—while its inverse function § 4-1 runs in the opposite direction (see Figure 1). These functions are then required to be smooth in the usual Euclidean sense defined above. This condition is con- sidered to hold trivially if u and do not meet. Č (UV) R" Ĕ(U) n(UV) R" S n(v) Figure 1. 1. Definition. An atlas A of dimension n on a space S is a collection of n-dimensional coordinate systems in S such that (A1) each point of S is contained in the domain of some coordinate system in, and (A2) any two coordinate systems in ✅ overlap smoothly. An atlas on S makes it possible to do calculus consistently on all of S. But different atlases may produce the same calculus, a technical difficulty eliminated as follows. Call an atlas Con S complete if C contains each co- ordinate system in S that overlaps smoothly with every coordinate system in C. 2. Lemma. Each atlas ✅ on S is contained in a unique complete atlas. Proof. If has dimension n, let A' be the set of all n-dimensional coordinate systems in S that overlap smoothly with every one contained in A. (a) A' is an atlas (of the same dimension as ✅).

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英語 高校生

わからないので教えてください。😭

B With a partner, take turns playing the roles of nurse and patient. Ask each other the questions you need to ask to fill out the application form below. One partner is Robert Jones, the other is Mary Woods. Robert William Jones D.O.B. 9/12/70 23-42 Shiizaki, Sakae-machi, Inba-gun, Chiba-ken, 289-1222 Tel.: 0475-72-1234 Businessman Stomachache Came to this hospital before with back pain in October, 2012 Mary Margaret Woods D.O.B. 7/31/80 7512 22nd Ave. N.W. Portland, Oregon 98115-4706 Tel.: (425) 791-8836 Housewife Sprained ankle First time at this hospital APPLICATION FORM Last Name month Date of Birth Address Telephone Occupation (Circle one) month Date First Name day year day year Middle Name Sex M / F years old Which department would you like to go to? (Circle one) 1 Self-employed 01 Internal Medicine 11 Obstetrics & Gynecology (OB/GYN) 2 Farmer/Skilled worker 02 Pediatrics 12 Ophthalmology (Eye doctor) 3 Civil servant 03 Surgery & Treatments 13 Dermatology (Skin doctor) 4 LO 00 5 6 Businessman Student Housewife 04 Orthopedics 14 Nutrition & Dietetics 05 Neurology 15 Radiology (X-ray) 06 Urology 16 Oral Surgery 7 Unemployed 07 Respiratory Medicine 17 Cardiology 8 Hospital employee 18 Plastic Surgery 08 Psychiatry 9 09 Otolaryngology (ENT) 19 Dentistry Other: (Please specify): 10 Anesthesiology 20 Allergy & Immunology 1. NO Have you ever been to this hospital before? 2. YES (Year: ) (Department: )

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