Abstract
For a locally compact Abelian (LCA) group G, let G + denote the group G endowed with its Bohr topology. With each piecewise affine map (defined below) α of G into another LCA group H, we show that there is associated a continuous map α + of G + into H + which coincides with α on a dense open subset of G +. We study when α + is a homeomorphism, provided that α has this property. These ideas are applied to investigate to what extent the group algebra of integrable functions on an LCA group G, L 1 ( G), characterizes the group.
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