Continuity

Let \( \mathbf{f}:X\mapsto\mathbb{R}^{m} \) be a function where \( X\subset\mathbb{R}^{n} \). We say that \( \mathbf{f} \) is continuous at \( \mathbf{a}\in X \) if \(\mathbf{a}\) is an isolated point of \(X\) or

\[ \lim_{\mathbf{x}\to\mathbf{a}} \mathbf{f}(\mathbf{x}) = \mathbf{f}(\mathbf{a}) \]