General topology Basic notions: open sets, neighbourhoods, bases Concept
Boundary
Summary
The boundary of a subset of a topological space is the set of points in its closure that are not in its interior. Each neighbourhood of a boundary point meets both the subset and its complement.
Where this leads
44 pages build on this one.
- Green's function for the Laplacian
- Phragmén–Lindelöf principle for subharmonic functions
- Jordan–Brouwer separation theorem
- Regular boundary point
- Zaremba's punctured ball
- Neumann problem
- Barrier
- Single layer potential
- Dirichlet problem
- Maximum principle for subharmonic functions
- Exterior cone condition
- Sub-mean value property
- Kakutani's solution of the Dirichlet problem
- Lipschitz domain
- Boundary integral method for the Dirichlet problem
- Supporting hyperplane theorem
- Dirichlet-to-Neumann operator
- Lebesgue spine
- Harmonic measure
- Resolutivity of boundary functions
- Straszewicz's theorem
- Curve of constant width
- Dynamical billiards
- Dirichlet boundary condition
- Illumination problem
- Double layer potential
- Jump relations for layer potentials
- Perron method
- Minkowski–Carathéodory theorem
- Calderón problem
- Neumann boundary condition
- Dirichlet's principle
- Wiener's criterion
- Inductive dimension
- Hadamard three-circle theorem for subharmonic functions
- Lindelöf's maximum principle
- Perron–Wiener–Brelot solution
- Kellogg–Evans theorem
- Harmonic measure as exit distribution
- Hadamard's two-constants theorem
- Method of fundamental solutions
- Supporting hyperplane
- Method of images
- Hartogs lemma for subharmonic functions
Further reading
- Web https://en.wikipedia.org/wiki/Boundary_(topology), lead section
About this page
| Tag | 05D5EGMFYV |
|---|---|
| URI | m2://05D5EGMFYV |
| Aliases | frontier, boundary-of-a-set |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54A05 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Green's function for the Laplacian
- Jordan–Brouwer separation theorem
- Regular boundary point
- Neumann problem
- Barrier
- Single layer potential
- Dirichlet problem
- Maximum principle for subharmonic functions
- Exterior cone condition
- Lipschitz domain
- Boundary integral method for the Dirichlet problem
- Supporting hyperplane theorem
- Resolutivity of boundary functions
- Curve of constant width
- Dynamical billiards
- Dirichlet boundary condition
- Illumination problem
- Double layer potential
- Jump relations for layer potentials
- Perron method
- Neumann boundary condition
- Dirichlet's principle
- Wiener's criterion
- Inductive dimension
- Perron–Wiener–Brelot solution
- Kellogg–Evans theorem
- Supporting hyperplane
- Method of images