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Transmission of continuity to the Bohr topology

✍ Scribed by Jorge Galindo; Salvador Hernández

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
539 KB
Volume
77
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

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) ck of G into another LCA group H, we show that there is associated a continuous map c~ + of G + imo H ÷ which coincides with on a dense open subset of G +. We study when ,~+ is a homeornorphism, provided that c~ has this property.

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

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