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Michael’s selection theorem for equicontinuous families of definable cells

Volume 133 / 2024

Filip Kołomyjec Annales Polonici Mathematici 133 (2024), 287-294 MSC: Primary 14P10; Secondary 14P15, 26E25, 54C65 DOI: 10.4064/ap240520-13-1 Published online: 21 January 2025

Abstract

We present an o-minimal version of Michael’s selection theorem. One variant of this theorem is known for definable multivalued mappings with closed $M$-Lipschitz cell values. We extend these results to include maps with values being standard definable cells. Furthermore, the Lipschitz condition is weakened to equicontinuity (in a sense given in the paper).

Authors

  • Filip KołomyjecFaculty of Mathematics and Computer Science
    Jagiellonian University
    30-348 Kraków, Poland
    e-mail

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