Computational topology for biomedical image and data analysis : theory and applications This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications Cover; Half Title; Series Page; Title Page; Copyright Page; Dedication; Contents; Series Preface; Foreword; Preface; Contributors; Authors; Section I: Theoretical foundations; Chapter 1: Elements of topology and homology; 1.1 ELEMENTS OF GROUP THEORY; 1.1.1 Set; 1.1.2 Group; 1.1.3 Ring and field; 1.1.4 Homomorphism; 1.1.5 Modular arithmetic; 1.2 TOPOLOGICAL SPACES; 1.2.1 Connected topological spaces; 1.2.2 Continuity and continuous maps; 1.3 METRIC SPACES; 1.3.1 Topology in a metric space; 1.4 ELEMENTS OF AFFINE VECTOR SPACES; 1.4.1 Affine vector space A; 1.5 SIMPLICIAL COMPLEXES