(The distance between two points is always less than or equal to the sum of distances through a third point).
Once a set is identified as a metric space, several foundational tools become available to study its structure: Fundamentals of Topologies & Metric Spaces - deep mind Metric Spaces
A is a set equipped with a "distance" function , called a metric , that assigns a non-negative real number to every pair of points in that set. This formalizes our intuitive idea of distance, allowing us to generalize concepts like limits, continuity, and convergence beyond the standard real number line. 1. The Formal Definition A metric space is a pair is a set and is a function such that for all , the following four axioms must hold: Non-negativity : Identity of Indiscernibles : if and only if Symmetry : Triangle Inequality : (The distance between two points is always less