In mathematics, a Zariski geometry consists of an abstract structure introduced by Ehud Hrushovski and Boris Zilber, in order to give a characterisation of the Zariski topology on an algebraic curve, and all its powers.
The Zariski topology on a product of algebraic varieties is very rarely the product topology, but richer in closed sets defined by equations that mix two sets of variables.
The result described gives that a very definite meaning, applying to projective curves and compact Riemann surfaces in particular.
The mappings defined by projecting out certain coordinates and setting others as constants are all continuous.
(K) For all pairs (x, y), (x′, y′) in X2, selected from outside a proper closed subset, there is some t in P such that the set of (t, u, v) in Q includes (t, x, y) and (t, x′, y′).