In topology, an open set is a fundamental concept that describes a collection of points in a space where, for every point in the set, there exists a surrounding area that also belongs to the set. This means that you can move a little in any direction from any point in the open set without leaving it. Open sets are crucial for defining continuity and limits in mathematics. Open sets can be found in various spaces, such as the real numbers ℝ or more complex structures like metric spaces. In the context of the real numbers, an example of an open set is an interval like (a, b), where a and b are not included. Understanding open sets helps in grasping more advanced topics in analysis and topology.