Examples of topological groups homeomorphic to 𝑙^{𝑓}₂

Abstract

Abstract.We prove that the following spaces are homeomorphic to 12'-(1) the group of piecewise continuous autotransformations of [-1,1] preserving Lebesgue measure, and (2) certain subgroups obtained as group spans of linearly independent arcs in linear spaces. These are consequences of our discussion of the problem whether o-fd-compact locally contractible metric groups must be either finite-dimensional or locally homeomorphic to l{.