EDB — 0HJ

[0HJ]Given $E\subseteq X$, we distinguish the points $x\in X$ in three distinct sets that are a partition of $X$.

• For every neighborhood $U$ of $x$, $U⧵\{x\}$ intersects $E$. These are the accumulation points of $E$.

• $x\in E$ and there is a neighborhood $U$ of $x$ such that $U\cap E=\{x\}$. These are the isolated points in $E$.

• Now describe the third set of points