[分析] 兩題問題
這是複變函數的問題:
1. Show that any point z of a domain is an accumulation point of that domain.
0
根據定義,這個集合(S)應該是 open and connected
如果用open的條件,可確定每一個點都是interior point,
則存在一個ε > 0, 使得 B (z ) ⊆ S
ε 0
應該不足以證明 z 是 accumulation point
0
而connected這個定義,我無法理解如何去運用它
2. Show that if z = x + iy , z = x + iy , then lim x = x
0 0 0 z->z 0
0
by the definition of limit.
我可以說:對於每一個ε > 0, 選 δ = ε,使得 |(x - x ) + i(y - y ) | < ε
0 0
=> 若 |z - z | = |(x - x ) + i(y - y ) | < δ = ε
0 0 0
則根據三角不等式, |x - x | ≦ |z - z | < ε
0 0
這樣行的通嗎?
邏輯有點不好,希望有一些熟悉這方面的人幫我解答
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