Order, lattices, ordered algebraic structures Binary relations and basic order notions Concept
Supremum
Summary
The supremum of a set is its least upper bound. It is an upper bound of the set that is less than or equal to every other upper bound. A set can have a supremum that is not an element of the set.
Where this leads
64 pages build on this one.
- Jordan measure
- Stokes' theorem
- Surface integral
- Orientable surface
- Cavalieri's principle
- Generalised Stokes theorem
- Divergence theorem
- Volume of a box
- Volume of a ball in R^3
- Surface area
- Flux through a surface
- Homotopy invariance of line integrals of closed forms
- Shell theorem
- Cheng–Yau gradient estimate
- Removable singularities for harmonic functions
- Compact element
- Harmonic majorant
- Scott topology
- Bourbaki–Witt theorem
- Way-below relation
- Conditionally complete lattice
- Smoothness and analyticity of harmonic functions
- Fenchel conjugate
- Varadhan's lemma
- Sub-mean value property
- Suslin's problem
- Kleene fixed-point theorem
- Hausdorff distance
- Standard part function
- Inner measure
- Join and meet
- Support function
- Davis's converse of the Knaster–Tarski theorem
- Algebraic lattice
- Scott domain
- Double layer potential
- Directed-complete partial order
- Koebe's theorem on the mean value property
- Omega-complete partial order
- Area-minimizing current
- Linear continuum
- Suslin line
- Compactness of families of harmonic functions
- McShane–Whitney extension
- Complete lattice
- Gradient estimates for harmonic functions
- Poisson integral formula
- Green's identities
- Least harmonic majorant
- Liouville's theorem for harmonic functions
- Packing measure
- Knaster–Tarski theorem
- Kantorovich–Rubinstein duality
- Liouville's theorem for planar harmonic functions
- Gauss's law for potentials
- Abian–Brown theorem
- Scott continuity
- Graph embedding
- Completeness in order theory
- Parabolic and hyperbolic Riemann surfaces
- Poisson integral for the half-space
- Bôcher's theorem
- Continuous lattice
- Hartogs lemma for subharmonic functions
Further reading
- Web https://en.wikipedia.org/wiki/Infimum_and_supremum, Formal definition
About this page
| Tag | 0R3H5PANRQ |
|---|---|
| URI | m2://0R3H5PANRQ |
| Aliases | least-upper-bound, sup |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A06 |
| Specializes | Upper bound |
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What links here
Used by
- Jordan measure
- Compact element
- Scott topology
- Bourbaki–Witt theorem
- Way-below relation
- Conditionally complete lattice
- Fenchel conjugate
- Varadhan's lemma
- Kleene fixed-point theorem
- Hausdorff distance
- Standard part function
- Inner measure
- Join and meet
- Support function
- Algebraic lattice
- Scott domain
- Directed-complete partial order
- Omega-complete partial order
- Linear continuum
- McShane–Whitney extension
- Complete lattice
- Packing measure
- Knaster–Tarski theorem
- Kantorovich–Rubinstein duality
- Abian–Brown theorem
- Scott continuity
- Completeness in order theory
- Continuous lattice