vix.ing · top · new · best · stats

On Borel structures in the Banach space C(βω)

2013/09/07 by Witold Marciszewski, Marciszewski, Witold, Grzegorz Plebanek +1
Mathematics · #46B26 #46E15 #54C35 #54H05 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis #math.FA #msc:46B26 #msc:46E15 #msc:54C35 #msc:54H05

paper · pdf · doi:10.48550/arxiv.1309.1908

14 pages

arxiv created 2013/09/07 · openalex publication_date 2013/09/07 · arxiv updated 2013/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related