Interpreting "formula_149" as a function that takes the value "f" mod "p" (i.e., the image of "f" in the residue field "R"/"p"), this subset is the locus where "f" is non-zero. The spectrum also makes precise the intuition that localisation and factor rings are complementary: the natural maps "R" → "R""f" and "R" → "R" / "fR" correspond, after endowing the spectra of the rings in question with their Zariski topology, to complementary open and closed immersions respectively. Even for basic rings, such as illustrated for "R" = Z at the right, the Zariski topology is quite different from the one on the set of real numbers.