Geometry of Euclidean Sets I: Vector, Topological, and Metric Aspects

The purpose of this first article is to propose answers to a fundamental question that arises in both theory and practice: which geometric models should be used to represent and study Euclidean sets of ${ℝ}_2^n$  ? It presents the first part of a comprehensive overview of geometry, branch by branch, focusing on vector, topological, and metric aspects. It summarizes the main ideas and concepts needed to rigorously address the modeling and geometric description of Euclidean sets, with numerous examples and illustrations in two and three dimensions.