An open set is a fundamental concept in topology, a branch of mathematics. In a given space, an open set is defined as a collection of points where, for every point in the set, there exists a surrounding area (or neighborhood) that also belongs to the set. This means you can move a little in any direction from any point in the set without leaving it. Open sets are crucial for understanding continuity and limits in real analysis. For example, in the real number line, an interval like (0, 1) is an open set because every point between 0 and 1 has a small range around it that also lies within the interval.