Representation of Group Isomorphisms: The Compact Case. (3rd February 2015) - Ferrer, Marita; Gary, Margarita; Hernández, Salvador
Abstract : LetG be a discrete group and letA andB be two subgroups ofG -valued continuous functions defined on two 0-dimensional compact spacesX andY . A group isomorphismH defined betweenA andB is called separating when, for each pair of mapsf,   g ∈ A satisfying thatf - 1 e G ∪ g - 1 e G = X, it holds thatH f - 1 e G ∪ H g - 1 e G = Y . We prove that under some mild conditions every biseparating isomorphismH : A → B can be represented by means of a continuous functionh : Y → X as a weighted composition operator. As a consequence we establish the equivalence of two subgroups of continuous functions if there is a biseparating isomorphism defined between them.