Re: [分析] 單點集合為閉集合?

[k6416337 (↖煞气a光希↘)]

※ 引述《sowter (saito)》之銘言：
: 假設一個單點(0,0)
: 我課本closed定義只有 E is closed if every limit point of E is a point of E
: 但單點是孤點
: 要怎麼說只有一個單點的集合是closed
: 麻煩解答感謝

p is a limit point of a set E <=> for all neighborhood N_p of p,there's a point
qεE,q≠p,such that qεN_p.[p.s. ε:belonging to]

Now,E={p=(0,0)} in |R^2 as "original PO" writes.
Clearly,every point rε|R^2\E is an exterior point of E and there is no other
point q≠p.So the set of limit points of E is ψ.
Since ψ＜E,E is closed.[p.s. ＜:contained in]

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◆ From: 140.113.178.13
※ 編輯: k6416337        來自: 140.113.178.13       (10/17 17:32)
→ sowter      :最後一句意思是所有極限點(空集)都為E的點嗎？
→ k6416337    :yes