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and radius is contained in

is a neighbourhood of a set if, for each element of there exists a positive number such that is contained in is called a uniform neighbourhood of a set if there exists a positive number such that for all elements of the open ball is contained in

Under the same condition of the uniform neighbourhood with the -neighbourhood of a set is the union of all the open balls of radius that are centered at each point in :

It directly follows that an -neighbourhood is

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