5.1. Open and Closed Sets

Proposition 5.1.7: Boundary, Accumulation, Interior, and Isolated Points

  • Let S R. Then each point of S is either an interior point or a boundary point.

  • Let S R. Then bd(S) = bd(R \ S).

  • A closed set contains all of its boundary points. An open set contains none of its boundary points.

  • Every non-isolated boundary point of a set S R is an accumulation point of S.

  • An accumulation point is never an isolated point.


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