metric topology

A metric topology is a way of defining how points are arranged and connected in a space using a distance measure, called a metric. It determines which points are close to each other based on this distance. For example, in regular 2D space, the usual distance formula creates a metric topology where neighborhoods are circles around points. This concept generalizes to any space where you can measure distance, allowing us to analyze concepts like continuity and convergence in a precise way that depends on how we define "closeness."