More on strong size properties

Abstract

Abstract. We continue our study of strong size maps. We show that strong size levels for the n-fold hyperspace of a continuum contain (n − 1)-cells. We give two constructions of strong size maps. We introduce reversible strong size properties. We prove that each of the following properties: being a continuum chainable continuum, being a locally connected continuum, and being a continuum with the property of Kelley, is a reversible strong size property. Following Professors Goodykoontz and Nadler, we define admissible strong size maps and show that the levels of admissible strong size maps for the n-fold hyperspace of a locally connected continuum are homeomorphic to the Hilbert cube. Professor Benjamín Espinoza defined Whitney preserving maps for the hyperspace of subcontinua of a continuum. We define strong size preserving maps and show that this class of maps coincides with the class of homeomorphisms.