The idea of topologizing an algebraic varietyV by choosing as closed sets the algebraic subvarieties of V can be used with good effect in order to topologize the set M* of all homomorphic mappings of any abstract field A into another abstract field K. In this general case we are dealing essentially with a generalization of the concept of the Riemann manifold of a field of algebraic functions ...
(1944). "The compactness of the Riemann manifold of an abstract field of algebraic functions". Bulletin of the American Mathematical Society50 (10): 683–691. ISSN0002-9904. DOI:10.1090/S0002-9904-1944-08206-2. (quote from p. 686)