On the splitting number and Mazurkiewicz’s theorem. (English) Zbl 0999.03043

Cichoń, Jacek; Żeberski, Szymon

Acta Univ. Carol., Math. Phys. 42, No. 2, 23-25 (2001).

Summary: We give a new proof of Mazurkiewicz’s theorem about bounded sequences of Borel functions. In this proof we use Shoenfield’s absoluteness theorem for \(\Sigma^1_2\)-sentences and one characterization of some class of sequentially compact topological spaces which involves the splitting number.

MSC:

03E15	Descriptive set theory
03E35	Consistency and independence results
54H05	Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)

Keywords:

perfect sets; bounded sequences of Borel functions; sequentially compact topological spaces; splitting number