Induced mappings on symmetric products of Hausdorff spaces

Abstract

Abstract The symbol 𝓕 n (X) denotes the hyperspace of all nonempty subsets of a Hausdorff space X having at most n points. This hyperspace is endowed with the Vietoris topology. For a mapping between Hausdorff spaces f : X → Y, define the induced mapping fn : 𝓕 n (X) → 𝓕 n (Y) by fn (A) = f(A) (the image of A under f). In this paper, we study the relationship between the condition f belongs to a class of mappings between Hausdorff spaces 𝕄 and the condition fn belongs to 𝕄.