→ k6416337:第一題就討論兩個點皆屬於不同的A、B就好 05/17 10:50
→ k6416337:但嚴謹來說，三種CASE都要討論到 有兩種是trivial 05/17 10:50
n
1. Let A and B be pathwise connected subset of R whose intersection A∩B is
nonempty. Prove that the union A∪B is also pathwise connected.
2
2. Show that the set { (x,y) in R | X^2 + y^4 = 1 } is pathwise connected.
2
3. Show that the set S = { (x,y) in R | either x or y is rational } is
pathwise connected.
以上三題我大概知道要怎麼證 , 但不知道要怎麼 " 寫 " , 麻煩版友寫一次給我看吧 .
還有 , 第一題需討論 x . y 皆屬於 A\B 或 B\A 的情形嗎 ?
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