[Thm]: Closed Set 與 Set of Accumulation Point 之關係:

設 $F\subseteq(M,d)$, 則 $F$ is closed $\Longleftrightarrow$ $\mathcal{L}(F)\subseteq F$

• [pf]:

[Thm]: Closure 與 Set of Accumulation Point 之關係:

$A\subseteq(M,d)$ 則 $Cl(A)=A\cup \mathcal{L}(A)$

• [pf]:

[Thm]: Closed Set 充要條件

$B\subseteq(M,d)$ is closed set $\Longleftrightarrow$ if $(x_n){n=1}^\infty\subseteq B$ and $\lim{n\rightarrow\infty}x_n=x$ then $x\in B$