Boundary (topology) - Common Definitions

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.

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