In mathematical Euclidean space, a small set of points surrounding and including a particular point. Thus, for an economic variable, such as an allocation, the neighborhood of a particular allocation includes all those allocations that are sufficiently similar to it.

An open set in a topological space that contains a specific point.

(Set-theoretical) topology starts with a definition of open sets which are often and interchangeably called neighborhoods. By definition, the empty set is open and so are finite intersections and arbitrary unions of open sets. A set is a topological space if some of its subsets are declared to be open subject to these conditions. An open set is a neighborhood of all its points. A function f:A-B from one topological space into another is continuous at a point aA if for every neighborhood V of f(a) there exists a neighborhood U of a such that f(U)V. This is equivalent to saying that inverse images of sets open in B are open in A. Complements of open sets are closed by definition.

A pixel and those surrounding pixels whose values are to be used in a processing operation that calculates a new value for the pixel.

A characteristic, specialized pattern of fasciculation among neurites (generated during process outgrowth) that causes individual neurites to be surrounded by a standard set of neighbors along a nerve cord or within neuropil; the pattern surrounding any particular nerve process is called its “neighborhood” ( White et al., 1983).