Click anywhere on the canvas to probe a point. The open ball around it reveals whether the point lies in the interior, on the boundary, or in the exterior of the set.
A point x is an interior point of S if there exists an open ball B(x, ε) entirely contained in S. The interior is the largest open set inside S.
x ∈ int(S) ⟺ ∃ε>0 : B(x,ε) ⊆ SA point x is a boundary point of S if every open ball B(x, ε) contains points both in S and in its complement Sᶜ.
x ∈ ∂S ⟺ ∀ε>0 : B(x,ε)∩S ≠ ∅ and B(x,ε)∩Sᶜ ≠ ∅A point x is an exterior point of S if there exists an open ball B(x, ε) entirely contained in Sᶜ. The exterior is the interior of the complement.
x ∈ ext(S) ⟺ ∃ε>0 : B(x,ε) ⊆ Sᶜ