Every idea

Ideas 6901–7050 of 7806.

Name	Kind	Subject
Hausdorff dimension	Concept	Measure and integration
Betti number	Concept	Algebraic topology
Boolean prime ideal theorem	Theorem	Mathematical logic and foundations
Inductive dimension	Definition	General topology
Moise's theorem	Theorem	Manifolds and cell complexes
Cusp form	Definition	Number theory
Non-atomic measure	Concept	Measure and integration
Isomonodromic deformation	Definition	Ordinary differential equations
Large sieve	Definition	Number theory
Valuation	Definition	Field theory and polynomials
Lindelöf space	Concept	General topology
Linearly disjoint extensions	Definition	Field theory and polynomials
Burkholder–Davis–Gundy inequality	Theorem	Probability theory and stochastic processes
Crossing number	Concept	Manifolds and cell complexes
Alexander–Spanier cohomology	Definition	Algebraic topology
Doob–Meyer decomposition theorem	Theorem	Probability theory and stochastic processes
Determinantal ideal	Concept	Commutative algebra
Secretary problem	Problem	Probability theory and stochastic processes
Banach limit	Concept	Sequences, series, summability
Euler characteristic	Definition	Algebraic topology
Matroid rank	Concept	Combinatorics
Dual matroid	Definition	Combinatorics
Lusternik–Schnirelmann theorem	Theorem	Algebraic topology
Kantorovich–Rubinstein duality	Theorem	Calculus of variations and optimal control; optimization
Manifold with corners	Concept	Global analysis, analysis on manifolds
Reduced ring	Concept	Commutative algebra
Ordinary point and singular point	Definition	Ordinary differential equations
Band matrix	Definition	Linear and multilinear algebra; matrix theory
Holomorphic map between Riemann surfaces	Concept	Functions of a complex variable
Mathieu groups	Object	Group theory and generalizations
Borel–Moore homology	Concept	Algebraic topology
Compositum of fields	Concept	Field theory and polynomials
Mean curvature	Definition	Differential geometry
Rate of convergence	Definition	Sequences, series, summability
Dimension of a polynomial ring	Theorem	Commutative algebra
Sylvester–Gallai theorem	Theorem	Convex and discrete geometry
Reidemeister's theorem	Theorem	Manifolds and cell complexes
Differential field	Definition	Field theory and polynomials
4-manifold	Definition	Manifolds and cell complexes
Nerve theorem	Theorem	Algebraic topology
The alternating group A3 is normal in S3	Example	Group theory and generalizations
Gelfand's spectral radius formula	Theorem	Functional analysis
Doléans-Dade exponential	Definition	Probability theory and stochastic processes
Gårding's inequality	Theorem	Partial differential equations
Ambrose–Singer theorem	Theorem	Differential geometry
n-sphere	Object	Manifolds and cell complexes
Descartes' rule of signs	Theorem	Real functions
Gorenstein ring	Concept	Commutative algebra
Topological modular forms	Definition	Algebraic topology
Turing reduction	Definition	Mathematical logic and foundations
Fractional calculus	Concept	Real functions
E-infinity operad	Concept	Algebraic topology
Generator of a semigroup	Definition	Operator theory
Stable theory	Concept	Mathematical logic and foundations
Inner function	Definition	Functions of a complex variable
Cobordism	Concept	Manifolds and cell complexes
Multivariate division algorithm	Concept	Commutative algebra
Bruhat decomposition	Theorem	Group theory and generalizations
Outer function	Definition	Functions of a complex variable
Pontryagin–Thom construction	Definition	Manifolds and cell complexes
Pointed space	Concept	Algebraic topology
Integral quadratic form	Definition	Number theory
Hölder summation	Definition	Sequences, series, summability
HNN extension	Definition	Group theory and generalizations
Error-correcting code	Concept	Information and communication theory, circuits
Tautological one-form	Definition	Differential geometry
Langevin equation	Definition	Probability theory and stochastic processes
Lévy–Prokhorov metric	Definition	Probability theory and stochastic processes
Picard–Vessiot extension	Concept	Field theory and polynomials
Saddle-node bifurcation	Definition	Ordinary differential equations
Space form	Definition	Differential geometry
Discriminant of a field extension	Definition	Number theory
Hamburger moment problem	Problem	Integral transforms, operational calculus
Krull's height theorem	Theorem	Commutative algebra
Universal Turing machine	Object	Mathematical logic and foundations
Systolic geometry	Definition	Differential geometry
Cotangent space of a local ring	Definition	Commutative algebra
Poisson kernel	Concept	Potential theory
Ehresmann connection	Concept	Differential geometry
Coupling	Definition	Probability theory and stochastic processes
Magnus expansion	Definition	Ordinary differential equations
Backward differentiation formula	Concept	Numerical analysis
Multiple integral	Definition	Real functions
Tietze transformations	Definition	Group theory and generalizations
Peixoto's theorem	Theorem	Dynamical systems and ergodic theory
Extremal length	Definition	Functions of a complex variable
Kaplansky density theorem	Theorem	Functional analysis
Invertible ideal	Definition	Commutative algebra
Tarski monster group	Object	Group theory and generalizations
Hirzebruch signature theorem	Theorem	Manifolds and cell complexes
Hopf invariant	Concept	Algebraic topology
Lagrange polynomial	Definition	Approximations and expansions
Resolvent	Definition	Operator theory
Finite ring	Definition	Associative rings and algebras
Aleph number	Definition	Mathematical logic and foundations
Descriptive set theory	Concept	Mathematical logic and foundations
Capacity of a set	Definition	Potential theory
Geometric realization	Concept	Algebraic topology
Block design	Definition	Combinatorics
Proof theory	Definition	Mathematical logic and foundations
Spectral triple	Definition	Global analysis, analysis on manifolds
Paley–Wiener theorem	Theorem	Functions of a complex variable
Random graph	Definition	Combinatorics
Normal form	Concept	Ordinary differential equations
The alternating group is the kernel of the sign	Example	Group theory and generalizations
Finitely presented group	Concept	Group theory and generalizations
Hyperreal number	Definition	Real functions
Schur product theorem	Theorem	Linear and multilinear algebra; matrix theory
Free product	Concept	Group theory and generalizations
Boundary value problem	Concept	Ordinary differential equations
Nevanlinna class	Definition	Functions of a complex variable
Degree of a continuous map	Concept	Algebraic topology
Semilocally simply connected space	Definition	Manifolds and cell complexes
Primary ideal	Concept	Commutative algebra
Friendship theorem	Theorem	Combinatorics
Laplacian matrix	Concept	Combinatorics
Computably enumerable set	Concept	Mathematical logic and foundations
Formal group law in topology	Concept	Algebraic topology
Baby Monster group	Object	Group theory and generalizations
Random graph	Concept	Combinatorics
Fundamental theorem of space curves	Theorem	Differential geometry
Whitehead link	Example	Manifolds and cell complexes
Proper map	Definition	General topology
Fejér's theorem	Theorem	Harmonic analysis on Euclidean spaces
Axiom of dependent choice	Definition	Mathematical logic and foundations
Simplicial approximation theorem	Theorem	Algebraic topology
Reverse mathematics	Definition	Mathematical logic and foundations
Closure of an operator	Concept	Operator theory
Pitchfork bifurcation	Definition	Ordinary differential equations
Sato–Tate conjecture	Theorem	Number theory
Hankel matrix	Definition	Linear and multilinear algebra; matrix theory
Gauss sum	Definition	Number theory
Gromov–Hausdorff convergence	Definition	Differential geometry
Pick matrix	Concept	Functions of a complex variable
Elimination theory	Definition	Commutative algebra
Logicism	Definition	Mathematical logic and foundations
Robinson arithmetic	Definition	Mathematical logic and foundations
Riesz representation theorem	Theorem	Functional analysis
Stokes phenomenon	Concept	Ordinary differential equations
Kolmogorov's three-series theorem	Theorem	Probability theory and stochastic processes
Bianchi identities	Theorem	Differential geometry
Parallel transport	Concept	Differential geometry
Orientability	Definition	Manifolds and cell complexes
Dual pair	Definition	Functional analysis
Poincaré recurrence theorem	Theorem	Dynamical systems and ergodic theory
Torsion tensor	Definition	Differential geometry
Cyclotomic extension	Definition	Field theory and polynomials
Finite type invariant	Concept	Manifolds and cell complexes
Continuous-time Markov chain	Concept	Probability theory and stochastic processes
Deck transformation group	Definition	Manifolds and cell complexes