High Quality Content by WIKIPEDIA articles! The concept of an open set is fundamental to many areas of mathematics, especially including point-set topology and metric topology. Intuitively speaking (see below for a more intuitive discussion), a set U is open if any point x in U can be moved by a small amount in any direction and still be in the set U. The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined. Concepts that use notions of nearness, such as the continuity of functions, can be translated into the language open sets.