※ 引述《james2009 (瑋仔)》之銘言：
: 1.suppose P不屬於E,Then P is a limit point <=> P is a boundary point of E.
: 2.P is a limit point of E => P is an interior point or a boundary point
: of E.
1.
=>
Since P belongs to the complement of E,
P belongs to the closure of the complement of E.
Since P is a limit point of E, P belongs to the closure of E.
Hence P is a boundary point of E.
<=
Since P is a boundary point of E, P belongs to the closure of E.
Since P belongs to the closure of E and P is not in E,
P is a limit point of E.
2.
Since P is a limit point of E, P belongs to the closure of E.
If P belongs to the closure of the complement of E,
then P is a boundary point of E.
If not, then there exists a neighborhood of P so that it is contained in E.
So P is an interior point of E.
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