A closed set is a concept in mathematics, particularly in topology. It is defined as a set that contains all its limit points. This means that if a sequence of points within the set approaches a certain point, that point must also be included in the set. For example, the set of all real numbers from 0 to 1, including 0 and 1, is a closed set. In contrast, an open set does not include its boundary points. Closed sets are important in various fields, including analysis, geometry, and functional analysis, as they help in understanding continuity and convergence within mathematical spaces.