Open Set Limits Definition

Definition

Suppose $f:D\subset {\mathbb{R}}^n\to {\mathbb{R}}^k$ where $D$ is an Open Set Suppose $x_0\in D$ Then, we say ${\lim }_{x\to x_0}f(x)=b$ if: $\forall$ Neighbourhood $N$ of $b$, $\exists$ Neighbourhood $U$ of $x_0$ s.t $(x\in U⟹f(x)\in N)$