High Quality Content by WIKIPEDIA articles! In mathematics, the ?-neighborhood (or epsilon-neighborhood) of a set A ? M, where (M, d) is a metric space, is the set of all points of M whose distance to some point of A is less than ? > 0. The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line connecting them.

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