Metric Spaces

A metric space is a mathematical concept in topology that defines a set of points equipped with a way to measure distances between them. Specifically, a metric is a function that takes any two points and gives a non-negative number representing the distance between them. This concept allows us to discuss properties like convergence, continuity, and compactness in a structured way. Metric spaces can describe familiar places like the surfaces of spheres or the more abstract realms of mathematical spaces, helping us understand how objects relate to each other in a measurable way.