In mathematics, the closure of a subset S in a topological space consists of all points which are intuitively "close to S". A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
For S a subset of a Euclidean space, x is a point of closure of S if every open ball centered at x contains a point of S (this point may be x itself).
This definition generalises to any subse...
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In mathematics, the closure of a subset S in a topological space consists of all points which are intuitively "close to S". A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
For S a subset of a Euclidean space, x is a point of closure of S if every open ball centered at x contains a point of S (this point may be x itself).
This definition generalises to any subset S of a metric space X. Fully expressed, for X a metric space with metric d, x is a point of closure of S if for every r > 0, there is a y in S such that the distance d(x, y)
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