Uniform space

A uniform space is a mathematical framework that generalizes the idea of "closeness" or "distance" beyond traditional metrics. It allows us to compare how similar points are in a space without necessarily assigning them a numerical distance. Instead, it uses collections of "entourages"—sets of pairs of points that are considered close—to define uniform properties like continuity and convergence. This concept is useful in analyzing spaces where a precise distance isn't available but a notion of uniform "closeness" still makes sense, providing structure for advanced analysis in topology and geometry.