= Solution
{c}
The <limit of a function> $f:E\to\mathbb R$ at a <limit point> $p$ of $E$ is $\ell$ when
$$
\forall\varepsilon>0\ \exists\delta>0\ \forall x\in E:\quad
0<|x-p|<\delta\ \Longrightarrow\ |f(x)-\ell|<\varepsilon.
$$
The <function> converges as $x\to p$ if such a finite $\ell$ exists. The puncture excludes any value assigned at $p$.
For $p\in E$, <continuity> at $p$ means
$$
\forall\varepsilon>0\ \exists\delta>0\ \forall x\in E:\quad
|x-p|<\delta\ \Longrightarrow\ |f(x)-f(p)|<\varepsilon.
$$
When $p$ is also a <limit point>, this says that the <limit of a function> is $f(p)$. At an <isolated point> of $E$, every <function> is <continuous> relative to $E$, even though the punctured limit does not have a unique forced value.
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