◀ ▲ ▶Branches / Topology / Definition: Boundary Points, Closures, Interiors, and Exteriors
Definition: Boundary Points, Closures, Interiors, and Exteriors
Let (X,\mathcal O) be a topological space and let B\subset X.
- A point A\in X is called a boundary point of B if every neighborhood N_A has points in common with B and also with the set complement B^C=X\setminus B.

- The set of all boundary points of B is called the boundary of the set B and denoted by \delta B.
- The closure B^- of B is the set union of B with its boundary B\cup \delta B.
- The interior B^\circ of B is the set difference of B without its boundary B\setminus \delta B.
- The exterior B^e of B is the set complement of the closure of B.
Mentioned in:
Definitions: 1 2 3 4
Explanations: 5
Proofs: 6 7 8 9
Propositions: 10 11 12
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References
Bibliography
- Forster Otto: "Analysis 2, Differentialrechnung im \mathbb R^n, Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984