Pontryagin duality for topological Abelian groups

✍ Scribed by Salvador Hernández

• Publisher: Springer-Verlag
• Year: 2001
• Tongue: French
• Weight: 119 KB
• Volume: 238
• Category: Article
• ISSN: 0025-5874
• DOI: 10.1007/s002090100263

✦ Synopsis

A topological Abelian group G is Pontryagin reflexive, or Preflexive for short, if the natural homomorphism of G to its bidual group is a topological isomorphism. We look at the question, set by Kaplan in 1948, of characterizing the topological Abelian groups that are P-reflexive. Thus, we find some conditions on an arbitrary group G that are equivalent to the P-reflexivity of G and give an example that corrects a wrong statement appearing in previously existent characterizations of P-reflexive groups.