2026-06-27T16:07:11Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1286962025-12-11T01:11:13Zcom_20.500.14352_14col_20.500.14352_15

Deville, Robert García Bravo, Miguel 2025-12-10T12:30:38Z 2025-12-10T12:30:38Z 2020 10.1112/mtk.12043 https://hdl.handle.net/20.500.14352/128696 https://doi.org/10.1112/mtk.12043 We show some new results about tilings in Banach spaces. A tiling of a Banach space Xis a covering by closed sets with non-empty interior, so that they have pairwise disjoint interiors. If,moreover, the tiles have inner radii uniformly bounded from below, and outer radii uniformly boundedfrom above, we say that the tiling is normal. In 2010, Preiss constructed a convex normal tiling ofthe separable Hilbert space. For Banach spaces with Schauder basis, we will show that Preiss’ resultis still true with starshaped tiles instead of convex ones. Also, whenever X is uniformly convex wegive precise constructions of convex normal tilings of the unit sphere, the unit ball or in general ofany convex body. eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 International Normal tilings of a Banach space and its ball journal article