\(M\)の集積点は明らかに\(M\)の触点である．
証明
\begin{align*}
&M-\{x\} \subset M\\
\Longleftrightarrow~&(M-\{x\})^{c} \supset M^{c}\\
\Longleftrightarrow~&(M-\{x\})^{ci} \supset M^{ci}\\
\Longleftrightarrow~&(M-\{x\})^{cic} \subset M^{cic}\\
\Longleftrightarrow~&(M-\{x\})^{a} \subset M^{a}\\
\Longleftrightarrow~&x \in \overline{M-\{x\}} \Rightarrow x \in M^{a}
\end{align*}
証明終