metric space theory

Metric space theory studies collections of points where a notion of distance between any two points is defined and satisfies certain rules (non-negativity, symmetry, triangle inequality, and distinguishing distinct points). It provides a framework to analyze how points relate spatially, generalizing familiar concepts like points on a line or in space to more abstract settings. This theory supports understanding convergence, continuity, and structure within various mathematical systems, and it’s fundamental in areas like analysis and topology, helping us understand how spaces behave and how to measure closeness or difference between elements in a rigorous way.