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On the real line, a neighbourhood of the real number a is an open interval (a−δ, a+δ), where δ>0, with its centre at a.

More generally, in a Euclidean or metric space it is the open set of all points whose distance d from a fixed point a is strictly less than a specified value, i.e. the set of points x for which d (x, a) < δ.

Subjects: Mathematics.

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