Re: [其他] 拓樸學證明
※ 引述《NTUEEboy ( ＮＴＵＥＥ)》之銘言：
: prove: An isolated point of S is a boundary point of S^c
: 不知道有沒解答一番
: 謝謝喔
Let p be an isolated point of S.
Then there exists a neighborhood B of p such that (B\{p})∩S is empty.
Hence B\{p} is contained in the complement of S.
For any neighborhood N of p, (N\{p})∩(B\{p}) is nonempty so (N\{p})∩S^c
containing (N\{p})∩(B\{p}) is nonempty.
Thus p is a limit point of S^c.
Moreover since p is not an interior point of S^c, we conclude that p is a
boundary point of S^c.
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