# Neighborhood

In mathematics, a neighborhood of a point is a subset of consisting of points that are within a given distance from . This is illustrated in the picture (from WIKIPEDIA), where the neighborhood of is a disk of a certain radius, centered at . Note that this interpretation of the term
where denotes the distance from to . We shall not dwell on properties of the distance function . For the purposes of this discussion it would suffice to assume that the neighborhoods induced by this function have the following two properties: In some areas of mathematics, neighborhoods are called balls. An analysis, e.g. Usually, the neighborhoods of interest are much smaller than the metropolitan set that contains them. |