Morphism of varieties

Definition
Let $$X$$ and $$Y$$ be two varieties over a field $$k$$ (which we usually assume to be algebraically closed). A morphism from $$X$$ to $$Y$$ is a continuous map $$\phi: X \to Y$$ such that:

For any open set $$V \subseteq Y$$ and any regular function $$f: V \to k$$ the map $$\phi \circ f: f^{-1}(V) \to k$$ is also a regular function.

Related notions

 * Rational map of varieties
 * Birational map of varieties
 * Isomorphism of varieties