推 shiang00 :感謝!!~~ 02/16 23:42
※ 引述《shiang00 (最近)》之銘言：
: 1. Let A,B,C, and D be subsets of R^2 (with the usual Euclidean metric).
: 下列三種情形,是否正確?為什麼? If it is always true, prove it.
: If it can be false, give a counterexample.
: (a.) If C ⊆ D, then cl(C) ⊆ cl(D)
: (b.) cl(A∩B) ⊆ cl(A)∩cl(B)
: (c.) A ⊆ cl(int(A))
2. Suppose f:R→R and that |f(x)-f(y)| <= 5|x-y| for all x and y in R.
Show that f is continuous on R.
Let e> 0 be given , choose a= e/5
Then |x-y| < a => |f(x)-f(y)| ≦ 5|x-y|< 5a < e
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◆ From: 122.125.3.5
※ 編輯: TaiwanFlight 來自: 122.125.3.5 (02/09 20:30)