Open and Closed Sets

In topology, an open set is like a region that doesn't include its boundary points, allowing you to move slightly within it without leaving. Think of an open disk; you can move anywhere inside without touching the edge. A closed set includes its boundary points, so you can approach its edges and remain within the set. For example, a closed disk contains its edge circle. These concepts help mathematicians understand how spaces are structured, with open sets focusing on interior points and closed sets including boundary points for a complete picture.