On Borel structures in the Banach space.

Abstract: M. Talagrand showed that, for the Čech–Stone compactification βω of the space of natural numbers ω, the norm and the weak topology generate different Borel structures in the Banach space . We prove that the Borel structures in generated by the weak and the pointwise topology are also different. We also show that in , where , there is no countable family of pointwise Borel sets separating functions from . [Copyright &y& Elsevier]