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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdŕ (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Ličge, Belgium)

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Pontryagin duality for spaces of continuous functions
by
Salvador Hernandez
Universidad Jaume I, Dpto. de Matemáticas, 12071-Castellón (Spain)
Coauthors: Vladimir Uspenskij (Ohio University, Athens, OH, USA)

A topological abelian group G is P-reflexive if the natural homomorphism of G to its Pontryagin bidual group is a topological isomorphism. Let Cp(X) be the space of continuous functions with the topology of pointwise convergence. We investigate for what spaces X the group Cp(X) is P-reflexive. We show that: (1) if Cp(X) is P-reflexive, then X is a P-space; (2) there exists a non-discrete space X such that Cp(X) is P-reflexive; (3) there exists a P-space X such that Cp(X) is not P-reflexive; (4) there exists a simple space X for which the question of whether Cp(X) is P-reflexive is undecidable in ZFC.

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Date received: February 14, 2000

Copyright © 2000 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 # caei-11.