List of selection theorems

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Short description: Wikipedia list article

This page lists selection theorems in mathematics.

Selection theorems for set-valued functions

Bressan–Colombo directionally continuous selection theorem
Castaing representation theorem
Fryszkowski decomposable map selection
Helly's selection theorem
Kuratowski and Ryll-Nardzewski measurable selection theorem
Michael selection theorem
Zero-dimensional Michael selection theorem
Robert Aumann measurable selection theorem
Yannelis-Prabhakar selection theorem^[1]

Selection theorems for set-valued sequences

Blaschke selection theorem

References

↑ Yannelis, Nicholas C.; Prabhakar, N. D. (1983-12-01). "Existence of maximal elements and equilibria in linear topological spaces". Journal of Mathematical Economics 12 (3): 233–245. doi:10.1016/0304-4068(83)90041-1. ISSN 0304-4068.

v t e Functional analysis (topics)
Topological vector spaces	Asplund Banach (list) Banach lattice Barrelled Bornological Brauner F-space Fréchet (tame) Hilbert (Inner product space Polarization identity) LF-space Locally convex (Seminorms/Minkowski functionals) Mackey Montel Nuclear Normed (norm) Quasinormed Reflexive Riesz Smith Stereotype Strictly convex Webbed Topological tensor product (of Hilbert spaces)
Topologies of function spaces	Dual Dual space (Dual norm) Operator Ultraweak Weak (polar operator) Mackey Strong (polar operator) Ultrastrong Uniform convergence
Linear operators	Adjoint Bilinear (form operator sesquilinear) (Un)Bounded Closed Compact (on Hilbert spaces) (Dis)Continuous Densely defined Fredholm Hilbert–Schmidt Functionals (positive) Normal Nuclear Self-adjoint Strictly singular Trace class Transpose Unitary
Operator theory	Banach algebras C-algebras Spectrum (C-algebra radius) Spectral theory (of ODEs Spectral theorem) Polar decomposition Singular value decomposition
Theorems	Banach–Alaoglu Banach–Mazur Banach–Saks Banach–Schauder (open mapping) Banach–Steinhaus (Uniform boundedness) Bessel's inequality Cauchy–Schwarz inequality Closed graph Closed range Eberlein–Šmulian Freudenthal spectral Gelfand–Mazur Gelfand–Naimark Goldstine Hahn–Banach (hyperplane separation) Kakutani fixed-point Krein–Milman Lomonosov's invariant subspace Mackey–Arens Mazur's lemma M. Riesz extension Riesz representation Parseval's identity Schauder fixed-point
Analysis	Abstract Wiener space Bochner space Differentiation in Fréchet spaces Derivatives (Fréchet Gateaux functional holomorphic) Integrals (Bochner Dunford Gelfand–Pettis regulated Paley–Wiener weak) Functional calculus (Borel continuous holomorphic) Inverse function theorem (Nash–Moser theorem) Measures (Lebesgue Projection-valued Vector) Weakly measurable function
Types of sets	Absolutely convex Absorbing Balanced Bounded Convex Convex cone (subset) Linear cone (subset) Radial Star-shaped Symmetric Zonotope
Subsets / set operations	Algebraic interior (core) Bounding points Convex hull Extreme point Interior Minkowski addition Polar

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