 The sets "A" and "B" need not be precisely separated by "f", i.e., we do not, and in general cannot, require that "f"("x") ≠ 0 and ≠ 1 for "x" outside of "A" and "B".The spaces in which this property holds are the perfectly normal spaces.Urysohn's lemma has led to the formulation of other topological properties such as the 'Tychonoff property' and 'completely Hausdorff spaces'.