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討論串[分析] 兩題高微
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Wade高微裡面的12.1有兩小題不知道該如何下手.... 想請教各位大大~感謝~. 12.1.2(b) In R^2, show that a countable set is not necessary a Jordan region.. 12.1.4 (b) Prove that Br(a)
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By inverse function theorem, f(R^n) is open.. Also {f(x_i)} is cauchy implies {x_i} is cauchy as. |x_i - x_j|C <= |f(x_i)-f(x_j)|.. This implies that
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n^2>n(n-1), 所以 1/n^2 <1/(n-1)- 1/n. 因此. x_(n+1) ≦ x_n + 1/(n-1)- 1/n. 可知. x_(n+1)+1/n ≦ x_n + 1/(n-1),. 定義數列y_(n)=x_(n+1)+1/n, n≧1。. 則y_(n)≧1/n>0 且y_(
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只做 f:|R^n → |R^n onto 部分的做法 給你看. 要證 onto 重點在於此例 {f(x_n)} cauchy => {x_n} cauchy ----- (1). 假設 0 不在 f(|R^n) (不失一般性). Let r = inf { || f(x) || | x 在 |R^
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