If I am given a map $f:U\subset \mathbb R^2 \to \mathbb R^3$ where $(x,y)\to (f(x,y),g(x,y),h(x,y))$. Is this necessarily a "parametrized surface"?
Am I right in thinking that any map of the above form satisfies the "parametrized" bit. Is it necessary a surface though?
Please correct me if I am wrong. Thank you.