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Neighborhood (mathematics)


In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior. Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set.

If is a topological space and is a point in , a neighbourhood of is a subset of that includes an open set containing ,


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