No I didn't the word range was in my first statement look
Your problem is you don't understand mathematical definitions correctly
Originally posted by ScimitarXEdge
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If S is a subset of X then a neighbourhood of S is a set V which includes an open set U containing S. It follows that a set V is a neighbourhood of S if and only if it is a neighbourhood of all the points in S. Furthermore, it follows that V is a neighbourhood of S iff S is a subset of the interior of V.
In a metric space M = (X,d), a set V is a neighbourhood of a point p if there exists an open ball with centre p and radius r, such that
is contained in V.
V is called uniform neighbourhood of a set S if there exists a positive number r such that for all elements p of S,
is contained in V.
For r > 0 the r-neighbourhood Sr of a set S is the set of all points in X which are at distance less than r from S (or equivalently, Sr is the union of all the open balls of radius r which are centred at a point in S).
is contained in V.
V is called uniform neighbourhood of a set S if there exists a positive number r such that for all elements p of S,
is contained in V.
For r > 0 the r-neighbourhood Sr of a set S is the set of all points in X which are at distance less than r from S (or equivalently, Sr is the union of all the open balls of radius r which are centred at a point in S).

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