Every idea

Ideas 4501–4650 of 7806.

Name	Kind	Subject
Zariski topology	Concept	Algebraic geometry
Residue field	Definition	Commutative algebra
Elementary abelian group	Definition	Group theory and generalizations
MV-algebra	Concept	Order, lattices, ordered algebraic structures
Contractible space	Definition	Algebraic topology
Cap product	Definition	Algebraic topology
Toeplitz–Hausdorff theorem	Theorem	Operator theory
Markov chain mixing time	Concept	Probability theory and stochastic processes
Singular integral operator	Definition	Harmonic analysis on Euclidean spaces
Liouville's theorem (differential algebra)	Theorem	Field theory and polynomials
The even integers form a subgroup of the integers	Example	Group theory and generalizations
Excluded point topology	Example	General topology
Elementary substructure	Concept	Mathematical logic and foundations
Property (T)	Definition	Topological groups, Lie groups
Summability method	Concept	Sequences, series, summability
Khinchin integral	Definition	Real functions
Tikhonov's theorem on slow-fast systems	Theorem	Ordinary differential equations
Non-Archimedean absolute value	Definition	Field theory and polynomials
Statistical convergence	Definition	Sequences, series, summability
Galois ring	Definition	Commutative algebra
Nash embedding theorems	Theorem	Differential geometry
Loop theorem	Theorem	Manifolds and cell complexes
Hall's theorem on solvable groups	Theorem	Group theory and generalizations
Derived set	Concept	General topology
Hopf degree theorem	Theorem	Algebraic topology
Series acceleration	Definition	Numerical analysis
Fractional ideal	Definition	Commutative algebra
Logarithm of a matrix	Definition	Linear and multilinear algebra; matrix theory
Clopen set	Definition	General topology
11/8 conjecture	Conjecture	Manifolds and cell complexes
Orientation of a manifold	Concept	Manifolds and cell complexes
Henselization	Concept	Commutative algebra
Stanley–Reisner ring	Concept	Commutative algebra
Supercompact cardinal	Concept	Mathematical logic and foundations
Formal group law in topology	Definition	Algebraic topology
Conway base 13 function	Counterexample	Real functions
Quotient of a normed space	Concept	Functional analysis
Borel functional calculus	Concept	Operator theory
Lyapunov equation	Concept	Linear and multilinear algebra; matrix theory
Finite field arithmetic	Definition	Field theory and polynomials
Pseudo algebraically closed field	Concept	Field theory and polynomials
Theory	Concept	Mathematical logic and foundations
Fixed-point property	Definition	General topology
Serre's theorem on regular local rings	Theorem	Commutative algebra
Suslin's theorem	Theorem	Mathematical logic and foundations
P-adic analysis	Definition	Functions of a complex variable
Finitely generated projective modules over local rings are free	Theorem	Commutative algebra
Ionescu-Tulcea theorem	Theorem	Probability theory and stochastic processes
Morse homology	Concept	Manifolds and cell complexes
Schur's inequality	Theorem	Real functions
Semi-continuity	Concept	Real functions
Cauchy matrix	Concept	Linear and multilinear algebra; matrix theory
System of parameters	Concept	Commutative algebra
Purely inseparable extension	Concept	Field theory and polynomials
Quasiregular map	Definition	Functions of a complex variable
Δ-complex	Definition	Algebraic topology
Difference quotient	Definition	Real functions
Principal bundle	Definition	Algebraic topology
Compact operator	Definition	Operator theory
Final topology	Definition	General topology
Sub-Riemannian manifold	Concept	Differential geometry
Exponential sum	Concept	Number theory
Ackermann function is not primitive recursive	Theorem	Mathematical logic and foundations
Structure	Concept	Mathematical logic and foundations
Sublinear function	Definition	Functional analysis
Foliation	Concept	Manifolds and cell complexes
Injective hull	Definition	Commutative algebra
Weierstrass product	Definition	Functions of a complex variable
Lebesgue covering dimension	Definition	General topology
Polynomial greatest common divisor	Definition	Commutative algebra
Isometry of Riemannian manifolds	Definition	Differential geometry
Hurwitz-stable matrix	Concept	Linear and multilinear algebra; matrix theory
Pettis integral	Concept	Measure and integration
Jacobi field	Concept	Differential geometry
Brunn–Minkowski theorem	Theorem	Convex and discrete geometry
Thurston norm	Concept	Manifolds and cell complexes
Class number	Definition	Number theory
Height of a prime ideal	Definition	Commutative algebra
Axiom schema of replacement	Definition	Mathematical logic and foundations
Coercive bilinear form	Definition	Operator theory
Subderivative	Concept	Real functions
Choquet integral	Definition	Measure and integration
Dirichlet L-function	Concept	Number theory
Finite morphism of rings	Definition	Commutative algebra
Zeros and poles	Definition	Functions of a complex variable
Incidence matrix	Concept	Combinatorics
Sullivan conjecture	Theorem	Algebraic topology
Internal set theory	Definition	Mathematical logic and foundations
Continuous functional calculus	Definition	Functional analysis
Permutation group	Definition	Group theory and generalizations
Cumulant	Concept	Probability theory and stochastic processes
Multiplication operator	Example	Operator theory
Drazin inverse	Concept	Linear and multilinear algebra; matrix theory
Calabi flow	Concept	Differential geometry
Laplace's method	Concept	Approximations and expansions
Hausdorff paradox	Counterexample	Measure and integration
Loewner order	Concept	Linear and multilinear algebra; matrix theory
Idele class group	Concept	Number theory
Δ-system lemma	Lemma	Mathematical logic and foundations
Convergence of filters	Definition	General topology
Completely normal space	Concept	General topology
Diffusion process	Concept	Probability theory and stochastic processes
Perturbation theory of linear operators	Definition	Operator theory
Pontryagin–Thom construction	Concept	Manifolds and cell complexes
Beltrami equation	Concept	Functions of a complex variable
Kummer's test	Theorem	Sequences, series, summability
Hilbert C*-module	Definition	Functional analysis
Banach manifold	Concept	Global analysis, analysis on manifolds
Tightness of measures	Definition	Probability theory and stochastic processes
Induced representation	Definition	Group theory and generalizations
Serre fibration	Definition	Algebraic topology
Second fundamental form	Concept	Differential geometry
Bihari–LaSalle inequality	Lemma	Real functions
Nuclear C*-algebra	Definition	Functional analysis
Galois cohomology	Concept	Field theory and polynomials
Nilpotence theorem	Theorem	Algebraic topology
Blaschke product	Concept	Functions of a complex variable
Proximal operator	Definition	Operations research, mathematical programming
Kalman rank condition	Theorem	Systems theory; control
Euler–Maclaurin formula	Theorem	Numerical analysis
Exponential type	Concept	Functions of a complex variable
Cartan's classification of symmetric spaces	Theorem	Differential geometry
Elimination theory	Concept	Commutative algebra
Potential theory	Concept	Potential theory
Field with one element	Concept	Algebraic geometry
Overdetermined system	Definition	Linear and multilinear algebra; matrix theory
Polycyclic group	Concept	Group theory and generalizations
Borel–Kolmogorov paradox	Counterexample	Probability theory and stochastic processes
Deligne–Lusztig theory	Definition	Group theory and generalizations
Contact process	Example	Probability theory and stochastic processes
Subfactor	Concept	Functional analysis
Almost complex manifold	Concept	Differential geometry
Liouville's theorem on phase-space volume	Theorem	Dynamical systems and ergodic theory
Schmidt subspace theorem	Theorem	Number theory
Handle decomposition	Concept	Manifolds and cell complexes
Seifert fiber space	Concept	Manifolds and cell complexes
Type	Concept	Mathematical logic and foundations
Spectral radius	Concept	Linear and multilinear algebra; matrix theory
Approximate identity	Definition	Functional analysis
Symmetric derivative	Definition	Real functions
Symmetric space	Definition	Differential geometry
Constructive analysis	Definition	Mathematical logic and foundations
Poincaré duality	Theorem	Algebraic topology
Z-group	Concept	Group theory and generalizations
Commuting probability	Definition	Group theory and generalizations
Pariah groups	Definition	Group theory and generalizations
Logarithmic capacity	Definition	Potential theory
Deduction theorem	Theorem	Mathematical logic and foundations
Elementary embedding	Definition	Mathematical logic and foundations
Homotopy	Concept	Algebraic topology