Page "Zariski topology" Paragraph 25

Every regular map of varieties is continuous in the Zariski topology.

In fact, the Zariski topology is the weakest topology ( with the fewest open sets ) in which this is true and in which points are closed.

This is easily verified by noting that the Zariski-closed sets are simply the intersections of the inverse images of 0 by the polynomial functions, considered as regular maps into