A normed space is a type of mathematical structure that consists of a vector space equipped with a function called a norm. This norm assigns a non-negative length or size to each vector in the space, allowing for the measurement of distances between vectors. The norm must satisfy specific properties, such as being positive, homogeneous, and satisfying the triangle inequality. In a normed space, the concept of convergence and continuity can be defined in terms of the norm. Common examples of normed spaces include Euclidean spaces and function spaces, where the norm can represent distances in various contexts, such as geometry or analysis.