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On non-injectivity of Borel functions selecting points from compact sets

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Abstract.

We show that no Borel function on the hyperspace of a compact metric space X, selecting points from nonempty closed sets in X, can be injective on a residual set in the hyperspace. As a consequence, we show that a measure-theoretic analogue of the marriage theorem for finite sets, obtained by R. D. Mauldin [7], [3], fails in the Baire category setting. This answers a question from [1].

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Authors and Affiliations

  1. Institute of Mathematics, Łódź Technical University, al. Politechniki 11, I-2, 90-924 Łódź, Poland, , , , , , PL

    M. Balcerzak<"a2"> & J. Peredko

  2. Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland, , , , , , PL

    R. Pol

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  1. M. Balcerzak<"a2">
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  2. J. Peredko
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  3. R. Pol
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Received: 19.8.1998

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Balcerzak<"a2">, M., Peredko, J. & Pol, R. On non-injectivity of Borel functions selecting points from compact sets. Arch. Math. 73, 286–290 (1999). https://doi.org/10.1007/s000130050400

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  • DOI: https://doi.org/10.1007/s000130050400

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