A reflexive admissible topological group must be locally compact
ELENA MARTIN PEINADOR1995, Proceedings of the American Mathematical Society
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Abstract
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This paper proves that a reflexive topological group is locally compact if and only if the evaluation mapping from the product of the group with itself into the torus is continuous. This result builds on Arens' theorem regarding admissible topologies in continuous functions and addresses a question previously posed by Megrelishvili. The work emphasizes the role of convergence spaces in establishing this characterization and highlights the distinction of locally compact Hausdorff abelian groups within the broader category of reflexive groups.
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