Exponential topology
There are examinated some properties of the hyperspace \(\psi\) X of all nonempty subsets of a topological space X with the exponential topology. For example, the authors describe a closure of a singleton of \(\psi\) X for a \(T_ 1\)-space X, prove that a singleton A of \(\psi\) X formed by closed points of X is \(\psi\) X-closed iff A is X-closed (without any assumption concerning X), show that X is \(T_ 0\) iff X is \(T_{1/2}\) (any singleton is either open or closed) and describe some other basic properties of \(\psi\) X with respect to corresponding properties of X.
scientific article; zbMATH DE number 3866152