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Session 36. Topology in Functional Analysis
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On Borel structures in function spaces |
Witold Marciszewski, University of Warsaw, Poland
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The talk is based on the joint works with Roman Pol and Grzegorz Plebanek
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Given a space \(C(K)\) of continuous real-valued functions on a compact space \(K\),
we shall consider the three \(\sigma\)-algebras of Borel sets in \(C(K)\) generated by the uniform topology, the weak topology, and the pointwise topology in \(C(K)\).
We will discuss some problems concerning these \(\sigma\)-algebras in \(C(K)\).
M. Talagrand showed that, for the Čech-Stone compactification
\(\beta\omega\) of the space of natural numbers \(\omega\), the norm
and the weak topology generate different Borel structures in \(C(\beta\omega)\). We prove that the Borel structures
in \(C(\beta\omega)\) generated by the weak and the pointwise
topology are also different.
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