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