In the foundational approach of André Weil, developed in his "Foundations of Algebraic Geometry", generic points played an important role, but were handled in a different manner. For an algebraic variety "V" over a field "K", "generic points" of "V" were a whole class of points of "V" taking values in a universal domain Ω, an algebraically closed field containing "K" but also an infinite supply of fresh indeterminates. This approach worked, without any need to deal directly with the topology of "V" ("K"-Zariski topology, that is), because the specializations could all be discussed at the field level (as in the valuation theory approach to algebraic geometry, popular in the 1930s).