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 ✅).

英語のこの並び替えを教えてください🙇🏻‍♀️

What do astronauts* see from their spaceship? (1)(look / space / like / does / what) to them? They see blackness around than TI

内容的には間違ってないか。文法は合っているか。の2点で英文を見てもらいたいです。全部で5文で、対話の穴埋め問題です。 ⤵︎ ⤵︎私が描きたかったことです。 1、電気を変えるのを手伝って欲しい 2、あなたの誕生日は2月25じゃなかった？(2月のスペルが間違ってます🙇‍♂️)... 続きを読む

II. 以下に指示された二人の対話を完成させるのに, 最もふさわしいと考えられる 英文を6語以上で書きなさい。 1) A: I'm thinking about changing the design of my bedroom. B: What were you thinking of doing? A: ( ) B: That will really brighten the atmosphere of the room. Let me know if you need a hand. : 2) A Hi, George. Happy birthday! B: Huh? What do you mean? It's not my birthday today. A: ( ) B: No, it's the 25th of March. But, that's okay. You can say it to me again next month. 3) A Did you hear that Tracey and Belinda decided to get married? B Yes, Belinda called me last night. It's wonderful news. We need to think about a present. A: ( ) B: That's a great idea; they both love entertaining at home. 4) A Why were you late this morning? B Well, there was no room to leave my bicycle at the station. A Really? Were all the spaces taken? B: Yes. I think people should be able to leave their bicycles anywhere. A: ( ) 5) A Don't you think John did really well in the debate contest? B: Yes, I was surprised. He is usually quite shy.

準一のライティングです。 ライティングが半分しか点数が取れないので頑張りたいです。 アドバイスお願いします。 Q, Is a marriage is becoming less important today than it was in the past? My mai... 続きを読む

この英作文の添削をお願いします！ テーマは 政府は宇宙探索にお金を使うべきか？ です！(ざっくりというと) 自分でスペル違うなって思ったところは治しました🙇‍♀️ 添削お願いします！

埼玉大文系前 2022年度 英語 23 Answer in a short essay between 120 and 150 words in English. Some people think governments should spend as much money as possible exploring outer space (for example, e, travelling to the Moon and to other planets). Other people disagree and think governments should spend this money taking care of our basic needs on Earth. Which of these two opinions do you agree with? Use specific reasons and details to support your answer.

高一 英語 疑問詞の問題です。 カッコに入る語が分かりません。 どなたか分かる方、教えて頂けませんでしょうか。 宇宙にいるのはどんな感じだろう。 （ ）（ ） it（ ）to be in space?

From space the seven continents look like little islands (as floating ）　in a giant sea. （）の中が間違っている理由を教えてください... it isが省略されていてitの中にはseven... 続きを読む

この写真のマーカーの部分 many thingsなのにthatと複数形にならないのはなぜですか

Soon our living space is filled with too many things: too many pairs of socks in our drawers, too many shoes in our closet. Books. Books. Books. That can be a source of frustration. Our belongings have turned out to be a real headache for us What should we do? Marie Kondo

問2.1の証明が分かりません。 ※1枚目が質問内容、2枚目が仮定

問 2.1 例1 (b), (c) で R" に定義された各種の距離 dp : R" × R” → [0,∞) (p = 1,2,...,∞) において, R” の点列 πm:= (x(m),x(m),...,xmm))∈R(m= R" 2 1,2,･･･) が, 点æ= (π1, 2,...,πn) ∈R" に収束するためには,各k ∈ {1, 2,...,n} に対し (m) →πk (m→8) となることが必要十分であることを示せ.

最後の文のwhat value is B(smellが入ります)の文構造を教えて頂きたいです。よろしくお願いします。

they can s example, follow coastlines and thr When they get very close 4 Mont to where they want to be, many use their sense of smell. anger as Homing pigeons give a clue to this. ("Homing" is not the same as migration. It suggests that pigeons can find their way home when taken by train or truck to some far-distant place and then released. But homing surely has some of the same mechanisms; migration does, and so can give clues to how it works.) It seems that as pigeons get fairly close to their home, they first pick up general smells that tell of bird dwellings-perhaps the general tempting stink of ammonia. As they get nearer, the smells become more specifically pigeon-like. Finally, as they get very close, they recognize the very particular odor of their own flock in its own space. More and more evidence is revealing that humans, too, have a wonderful awareness of odor, even if they do not consciously recognize it, such that they find particular men or women attractive or disgusting according to their primitive substances such as sweat no doubt a cooling thought for human beings have risen above such things. We do not those who like to suppose that (2) normally think of birds as creatures that attach importance to smell, but many of them 。 do, in many contexts. 112055見る形 137. ho doubt, but なるほしだが、 But what use are A clues when a bird is above some apparently boundless ocean? What value is (B) when it is a thousand miles from where it wants to be? What else is there? O is value. air force, havy, army. doy and the moon