Geometry of Euclidean Sets II: Analytical, Random, and Hypertopological Aspects

The purpose of this second 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 second part of a comprehensive overview of geometry, branch by branch, focusing on analytical, stochastic, and hypertopological aspects. It summarizes the main ideas and concepts necessary for a rigorous treatment of the modeling and geometric description of Euclidean sets, with numerous examples and illustrations in two and three dimensions.