In mathematics, a neighbourhood of a point is roughly a set of points which are "close" to it. If working in a metric space, the usual meaning of "neighbourhood of a" is "an open ball centred at a". More generally, in a topological space, "neighbourhood of a" means "a set containing an open set which contains a".

Neigh"bor*hood (?), n. [Written also neighbourhood.]


The quality or condition of being a neighbor; the state of being or dwelling near; proximity.

Then the prison and the palace were in awful neighborhood. Ld. Lytton.


A place near; vicinity; adjoining district; a region the inhabitants of which may be counted as neighbors; as, he lives in my neighborhood.


The inhabitants who live in the vicinity of each other; as, the fire alarmed all the neiborhood.


The disposition becoming a neighbor; neighborly kindness or good will.


Jer. Taylor.

Syn. -- Vicinity; vicinaty; proximity. -- Neighborhood, Vicinity. Neigborhood is Anglo-Saxon, and vicinity is Latin. Vicinity does not commonly denote so close a connection as neighborhood. A neigborhood is a more immediately vicinity. The houses immediately adjoining a square are in the neighborhood of that square; those which are somewhat further removed are also in the vicinity of the square.


© Webster 1913.

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