In a single variable case, we know that $f$ is continuous at $c$ if and only if $$\lim_{x \to c}f(x)=f(c).$$
My question is does this property still holds in a multi variable case. For example, let $f:D\subset R^4 \to R$, and $(a,b,c,d)$ be a cluster point of $D$. Then, $f$ is continuous at $(a,b,c,d)$ if and only if$$\lim_{(x,y,z,s)\to(a,b,c,d)}f(x,y,z,s)=f(a,b,c,d).$$
Thank you in advance.