[Banach] Abstract of a paper by Witold Marciszewski and Grzegorz Plebanek

This is an announcement for the paper "On Borel structures in the Banach space C(\beta\omega)" by Witold Marciszewski and Grzegorz Plebanek.

Abstract: M. Talagrand showed that, for the Cech-Stone compactification \beta\omega\ of the space of natural numbers, the norm and the weak topology generate different Borel structures in the Banach space C(\beta\omega). We prove that the Borel structures in C(\beta\omega) generated by the weak and the pointwise topology are also different. We also show that in C(\omega*), where \omega*=\beta\omega - \omega, there is no countable family of pointwise Borel sets separating functions from C(\omega*).

Archive classification: math.FA

Mathematics Subject Classification: 46B26, 46E15, 54C35, 54H05

Remarks: 14 pages

Submitted from: grzes@math.uni.wroc.pl

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1309.1908

or

http://arXiv.org/abs/1309.1908