Michael’s selection theorem for equicontinuous families of definable cells
Annales Polonici Mathematici
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).
