On Continuity Transmission to the Bohr Topology
by
Jorge Galindo Pastor
Univesidad Jaume I
Coauthors: Salvador Hernández Muñoz

Given two abelian groups G and H , a map \alpha of G into H is (algebraically) piecewise affine when G = \cup _{i = 1}ⁿ S_i, S_i subset or equal K_i for K_i, an open coset in G and there is for every i = 1 ... n an affine map \alpha_i : K_i --> H coinciding with \alpha on S_i.

For a locally compact abelian group (LCA ), let G⁺ denote the group G endowed with its Bohr topology.

With each piecewise affine map \alpha of G into another LCA group H, we show that there is associated a continuous map \alpha⁺ of G⁺ into H⁺ which coincides with \alpha on a dense open set of G⁺. We study when \alpha⁺ is a homeomorphism, provided that \alpha has this property.

These ideas are applied to investigate to what extent the group algebra of integrable functions on a LCA group G, L¹(G), characterizes the group.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaf-62.