Normal and starlike tilings in separable Banach spaces

TL;DR

This paper constructs a universal tiling in any separable Banach space where each tile is starlike, contains a fixed-radius ball, and is contained within a larger ball, highlighting a uniform geometric structure.

Contribution

It introduces a universal tiling with starlike tiles in all separable Banach spaces, with uniform size bounds, advancing geometric tiling theory.

Findings

Existence of a universal tiling in all separable Banach spaces

Tiles are starlike and uniformly bounded in size

Each tile contains and is contained within fixed-radius balls

Abstract

In this note, we provide a starlike and normal tiling in any separable Banach space. That means, there are positive constants r and R (not depending on the separable Banach space) such that every tile of this tiling is starlike, contains a ball of radius r and is contained in a ball of radius R.