One can thus view the topological space formula_1 as an "enrichment" of the topological space "A" (with Zariski topology): for every subvariety of "A", one additional non-closed point has been introduced, and this point "keeps track" of the corresponding subvariety. One thinks of this point as the generic point for the subvariety. Furthermore, the sheaf on formula_1 and the sheaf of polynomial functions on "A" are essentially identical. By studying spectra of polynomial rings instead of algebraic sets with Zariski topology, one can generalize the concepts of algebraic geometry to non-algebraically closed fields and beyond, eventually arriving at the language of schemes.