On Borel Sets in Function Spaces with the Weak Topology |
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| Authors: | Burke Dennis K; Pol Roman |
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| Institution: | Department of Mathematics, Miami University Oxford, OH 45056, USA burkedk{at}muohio.edu
Faculty of Mathematics, Informatics and Mechanics, Warsaw University Banacha 2, 02-097 Warszawa, Poland pol{at}mimuw.edu.pl |
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| Abstract: | It is proved that the duality map  , :(  , weak)x(()*, weak*) R isnot Borel. More generally, the evaluation e:(C)(K),x KR, e(f,x) = f(x), is not Borel for any function space C(K) on a compactF-space. It is also shown that a non-coincidence of norm-Boreland weak-Borel sets in a function space does not imply thatthe duality map is non-Borel. |
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