One-to-one Borel selection theorems

Balcerzak, Marek; Peredko, Joanna

doi:10.1090/S0002-9939-99-04784-X

One-to-one Borel selection theorems
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by Marek Balcerzak and Joanna Peredko PDF

Proc. Amer. Math. Soc. 127 (1999), 2759-2766 Request permission

Abstract:

For $X=[0,1]$ we obtain new theorems stating that a Borel set in $X^2$ with large sets of large vertical and large horizontal sections admits a one-to-one Borel selection with large domain and large range. Largeness is meant mainly in measure or category sense. Our proofs combine a result of Graf and Mauldin with a modified result of Sarbadhikari.

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