Convex and discrete geometry Convex sets: basic notions Concept
Convex set
Summary
A set of points is convex if it contains the whole segment between each two of its points. A solid ball and a solid cube are convex; a crescent is not.
Where this leads
75 pages build on this one.
- Convex hull
- Jung's theorem
- Strictly convex set
- Lempert's theorem on convex domains
- Lyapunov's convexity theorem
- Birkhoff–von Neumann theorem
- Michael selection theorem
- Céa's lemma
- Minkowski's second theorem
- Ryll-Nardzewski fixed-point theorem
- Hahn–Banach separation theorem
- Variational inequality
- Barrelled space
- Schaefer's fixed point theorem
- Kakutani fixed-point theorem
- Face of a convex set
- Kolmogorov's normability criterion
- Lax–Milgram theorem
- Toeplitz–Hausdorff theorem
- Bolza problem
- Uniqueness of best approximation in strictly convex spaces
- Gauss–Lucas theorem
- Minimum total potential energy principle
- Birkhoff polytope
- Leray–Schauder method
- Mackey topology
- Locally convex space
- Centerpoint theorem
- Cauchy's rigidity theorem
- Newton polygon
- Blaschke selection theorem
- Schauder fixed-point theorem
- Hilbert space adjoint
- Supporting hyperplane theorem
- Optimal control of partial differential equations
- Successive minima
- Bornological space
- Straszewicz's theorem
- Helly's theorem
- Gage–Hamilton–Grayson theorem
- Obstacle problem
- Empirical likelihood
- Lions–Stampacchia theorem
- Hilbert metric
- LF-space
- Convex cone
- Hilbert projection theorem
- Stefan problem as a variational inequality
- Lomonosov's invariant subspace theorem
- Schauder fixed-point theorem for integral equations
- Fractional Helly theorem
- Complete class theorem
- Convex join
- Galerkin method
- Brouwer fixed-point theorem
- Logarithmically convex domain
- Minkowski–Carathéodory theorem
- Krein–Smulian theorem
- Choquet theory
- Bishop–Phelps theorem
- Happy ending problem
- Signorini problem
- Ky Fan minimax inequality
- Bang–bang control
- Krein–Milman theorem
- Ladyzhenskaya–Babuška–Brezzi condition
- Relaxed control
- Lebesgue's universal covering problem
- Riesz representation theorem
- Extreme point
- Convenient vector space
- Filippov's existence theorem
- Kirchberger's theorem
- Numerical range
- Convex body
Further reading
- Web https://en.wikipedia.org/wiki/Convex_set, lead section
About this page
| Tag | 02AS45T3H9 |
|---|---|
| URI | m2://02AS45T3H9 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 52A20 |
| Same as |
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What this page needs for W2
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What links here
Definitions
Used by
- Convex hull
- Strictly convex set
- Lempert's theorem on convex domains
- Lyapunov's convexity theorem
- Michael selection theorem
- Minkowski's second theorem
- Ryll-Nardzewski fixed-point theorem
- Hahn–Banach separation theorem
- Variational inequality
- Barrelled space
- Kakutani fixed-point theorem
- Face of a convex set
- Kolmogorov's normability criterion
- Toeplitz–Hausdorff theorem
- Uniqueness of best approximation in strictly convex spaces
- Mackey topology
- Locally convex space
- Centerpoint theorem
- Cauchy's rigidity theorem
- Blaschke selection theorem
- Schauder fixed-point theorem
- Supporting hyperplane theorem
- Optimal control of partial differential equations
- Successive minima
- Bornological space
- Straszewicz's theorem
- Helly's theorem
- Gage–Hamilton–Grayson theorem
- Obstacle problem
- Lions–Stampacchia theorem
- Hilbert metric
- LF-space
- Convex cone
- Hilbert projection theorem
- Fractional Helly theorem
- Complete class theorem
- Convex join
- Brouwer fixed-point theorem
- Logarithmically convex domain
- Minkowski–Carathéodory theorem
- Krein–Smulian theorem
- Choquet theory
- Bishop–Phelps theorem
- Happy ending problem
- Ky Fan minimax inequality
- Bang–bang control
- Krein–Milman theorem
- Lebesgue's universal covering problem
- Extreme point
- Filippov's existence theorem
- Kirchberger's theorem
- Convex body