From Wikipedia:
Suppose $X,Y$ are topological spaces with $Y$ a Hausdorff space. Let $p$ be a limit point of $Ω⊆X$, and $L ∈Y$. For a function $f : Ω → Y$, it is said that the limit of $f$ as $x$ approaches p is L (i.e., $f(x)→L$ as $x→p$) and write $ \lim_{x \to p}f(x) = L $ if for every open neighborhood $V$ of $L$, there exists an open neighborhood $U$ of $p$ such that $f(U∩Ω- \{p\}) ⊆ V$.
I wonder if people also often generalize the definition of a limit of a function $f$ to the case when $p$ is an isolated point of $\Omega$?
Can the above definition except that $p$ is a limit point of $\Omega$ can be applied to the case when $p$ is an isolated point of $\Omega$?
Specifically, is the "openness" of $V$ wrt the topology of $X$ or wrt the subspace topology on $\Omega$?
Thanks and regards!