 For example, a corollary of the lemma is that normal "T"1 spaces are Tychonoff.The procedure is an entirely straightforward application of the definition of normality (once one draws some figures representing the first few steps in the induction described below to see what is going on), beginning with two disjoint closed sets.The "clever" part of the proof is the indexing of the open sets thus constructed by dyadic fractions.