Non-uniformly continuous nearest point maps Medina Sabino, Rubén Quilis, Andrés We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any non-singleton compact and convex subset is continuous but not uniformly continuous. The space we construct is locally uniformly convex, which ensures the continuity of all these nearest point maps. Moreover, we prove that every infinitedimensional separable Banach space is arbitrarily close (in the Banach-Mazur distance) to one satisfying the above conditions. 2024-11-04T13:08:02Z 2024-11-04T13:08:02Z 2024-10-02 journal article Medina Sabino, R. & Quilis, A. Proc. Amer. Math. Soc. 152 (2024), 5137-5148. [https://doi.org/10.1090/proc/16916] https://hdl.handle.net/10481/96618 10.1090/proc/16916 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional American Mathematical Society