Common Definitions
There are several common (and equivalent) definitions to the boundary of a subset S of a topological space X:
- the closure of S without the interior of S: ∂S = S \ So.
- the intersection of the closure of S with the closure of its complement: ∂S = S ∩ (X \ S).
- the set of points p of X such that every neighborhood of p contains at least one point of S and at least one point not of S.
Read more about this topic: Boundary (topology)
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