👉 Reaches, in mathematics and computer science, refers to the set of all points that can be connected to a given set of points by a sequence of moves, typically using a finite set of rules or operations. These moves can include moving from one point to another, combining points through unions (like in set theory), or applying transformations. The reach of a set is the smallest set of points that can generate all points in the original set through these operations. For example, in graph theory, the reach of a vertex is the set of vertices that can be reached from it by moving along edges, often defined as all vertices within a certain distance (e.g., one or two steps). In more abstract settings, like in the context of function spaces or topological spaces, reaches help define the boundaries and connectivity properties of these spaces. Reaches are fundamental in understanding how structures are built from simpler components and play a crucial role in areas like network analysis, data mining, and algorithm design.
