Regular G(Delta)-Diagonals And Hyperspaces

In this paper, we mainly prove that open k-to-one maps need not inversely preserve regular G(delta)-diagonals (or zero-set diagonals), and open k-to-one maps preserve zero-set diagonals. If X is continuously semi-metrizable, then the Vietoris hyperspace F(X) is also continuously semi-metrizable. For a Hausdorff space X, the Pixley-Roy hyperspace F-2[X] has a regular G(delta)-diagonal if and only if each point of X is a G(delta)-set. (C) 2020 Elsevier B.V. All rights reserved.