The density topology is not generated (Q809202)

A topological space (X,t) is generated if for each topology \(t'\) such that the set of continuous functions \(f: (X,t')\to (X,t')\) contains the set of all continuous functions \(f: (X,t)\to (X,t)\) we have also \(t'\supset t\). Using the characterization of generated spaces given by \textit{J. C. Warndorf} [Fundam. Math. 66, 25-43 (1969; Zbl 0189.232)] the authors have proved that the density topology is not generated.