A closed set is a concept from mathematics, particularly in the field of topology. It refers to a set that contains all its limit points. This means that if you take any point that is close to the set, that point will also be included in the set. For example, in the set of real numbers, the interval [0, 1] is closed because it includes both endpoints, 0 and 1. In contrast, an open set does not include its boundary points. Understanding closed sets is essential for various mathematical applications, including calculus and analysis, where concepts like continuity and convergence are explored. The distinction between closed and open sets helps in studying the properties of spaces in topology.