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

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.


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