Continuous function
Summary
A continuous function is a function that is continuous at each point of its domain. Small changes of the argument then give small changes of the value. The node continuous function gives the precise definition.
Where this leads
151 pages build on this one.
- Nonlinear Volterra equation
- Krylov–Bogolyubov theorem
- Continuous additive functions are linear
- Ergodic decomposition
- Urysohn integral equation
- Phragmén–Lindelöf principle for subharmonic functions
- Namioka--Phelps
- L2 convergence of Fourier series
- Regular boundary point
- Removable singularities for harmonic functions
- Milnor–Thurston kneading theory
- Ill-posedness of real Laplace inversion
- Characterization of Shannon entropy
- Wiener–Khinchin theorem
- Neural network approximation
- Kahane–Katznelson theorem
- Regula falsi
- Pointless topology
- Dini–Lipschitz criterion
- Homotopy fiber
- Zaremba's punctured ball
- Fiber bundle
- Quadrature rule
- Continuous kernel
- Brent's method
- Involution as solution of Babbage's equation
- Quasi-arithmetic mean
- Modulus of smoothness
- Neumann problem
- Locale
- Semiconjugacy and factor map
- Rational approximation
- Tychonoff space
- Space of functions vanishing at infinity
- Schaefer's fixed point theorem
- Bisection method
- Barrier
- Donsker's theorem
- Dirichlet problem
- Root-finding algorithm
- Homotopy lifting property
- Fixed-point property
- Continuous functional calculus
- Serre fibration
- Kolmogorov–Nagumo characterization of quasi-arithmetic means
- Brelot space
- Maximum principle for subharmonic functions
- du Bois-Reymond lemma
- Summability kernel
- Leray–Schauder method
- Monad in nonstandard topology
- Varadhan's lemma
- Weakly singular kernel
- Wiener filter equation
- Sub-mean value property
- Cohomology operation
- Müntz–Szász theorem
- Wiener algebra
- Kakutani's solution of the Dirichlet problem
- Continuous mapping theorem
- Lyapunov function for a difference equation
- Converse of the mean value property
- Uniform convergence of absolutely summable Fourier series
- Topological conjugacy
- Space of bounded continuous functions
- Uniform algebra
- Boundary integral method for the Dirichlet problem
- Schauder fixed-point theorem
- Dirichlet-to-Neumann operator
- Riesz–Markov–Kakutani representation theorem
- Perfectly normal space
- Littlewood's three principles
- Harmonic measure
- FK-space
- Resolutivity of boundary functions
- Cauchy formula for repeated integration
- Attractor
- Optimal control
- Midpoint convex function
- Discontinuous additive functions via a Hamel basis
- Continuous function with divergent Fourier series
- de Rham curve
- Well-posed problem
- Slutsky's theorem
- Bohr's approximation theorem
- Lusin's theorem
- Variational principle for topological entropy
- Universal approximation theorem
- Chebyshev system
- Jump relations for layer potentials
- Lomonosov's invariant subspace theorem
- Schauder fixed-point theorem for integral equations
- Local trivialization
- Weak convergence of measures
- Existence and uniqueness of Haar measure
- Density of trigonometric polynomials in continuous functions
- Linear integral equation
- Unique ergodicity
- Partition of unity
- Koebe's theorem on the mean value property
- Spline
- Bohr almost periodic function
- Perron method
- Bernstein–Doetsch theorem
- Compactness of families of harmonic functions
- Integral equation of the third kind
- Minimax approximation
- Fourier basis of L2 of the circle
- Poisson integral formula
- Modular function
- Butterfly effect
- Hahn–Mazurkiewicz theorem
- Least harmonic majorant
- Space-filling curve
- Galois representation
- Linking number
- Calderón problem
- Dirichlet's principle
- Mean-periodic function
- Lebesgue constants of the Dirichlet kernel
- Suspension flow
- Remez algorithm
- Scott continuity
- Bifurcation in a family of maps
- Hadamard three-circle theorem for subharmonic functions
- Lindelöf's maximum principle
- Basel problem via Fourier series
- BK-space
- Ridders' method
- Nyström method
- Kolmogorov–Arnold representation theorem
- Harmonic measure as exit distribution
- Hilbert's thirteenth problem
- Poisson integral for the half-space
- Jensen inequality as a functional inequality
- Harmonic space
- Hadamard's two-constants theorem
- Skorokhod's embedding theorem
- Decay of Fourier coefficients and smoothness
- Schwarz reflection principle for harmonic functions
- Method of fundamental solutions
- Bôcher's theorem
- Almost periodic function
- Sierpiński's theorem on measurable midpoint convex functions
- Approximation by convolution with mollifiers
- Loewner differential equation
- Cauchy's functional equation
- Hartogs lemma for subharmonic functions
- Green's function
- Weighted polynomial approximation
- Faber's theorem on interpolation
Further reading
- Web https://en.wikipedia.org/wiki/Continuous_function, lead section
About this page
| Tag | 0X3WGX95FE |
|---|---|
| URI | m2://0X3WGX95FE |
| Kind | concept |
| Writing | W1 stated |
| MSC | 26A15 |
| Same as |
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- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Instances
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Used by
- Nonlinear Volterra equation
- Krylov–Bogolyubov theorem
- Continuous additive functions are linear
- Urysohn integral equation
- Regular boundary point
- Milnor–Thurston kneading theory
- Characterization of Shannon entropy
- Wiener–Khinchin theorem
- Neural network approximation
- Kahane–Katznelson theorem
- Regula falsi
- Pointless topology
- Dini–Lipschitz criterion
- Homotopy fiber
- Fiber bundle
- Quadrature rule
- Continuous kernel
- Involution as solution of Babbage's equation
- Quasi-arithmetic mean
- Modulus of smoothness
- Neumann problem
- Locale
- Semiconjugacy and factor map
- Rational approximation
- Tychonoff space
- Space of functions vanishing at infinity
- Schaefer's fixed point theorem
- Bisection method
- Barrier
- Donsker's theorem
- Dirichlet problem
- Root-finding algorithm
- Homotopy lifting property
- Fixed-point property
- Continuous functional calculus
- Serre fibration
- Kolmogorov–Nagumo characterization of quasi-arithmetic means
- Brelot space
- du Bois-Reymond lemma
- Summability kernel
- Leray–Schauder method
- Monad in nonstandard topology
- Varadhan's lemma
- Weakly singular kernel
- Cohomology operation
- Müntz–Szász theorem
- Wiener algebra
- Continuous mapping theorem
- Lyapunov function for a difference equation
- Converse of the mean value property
- Uniform convergence of absolutely summable Fourier series
- Topological conjugacy
- Space of bounded continuous functions
- Uniform algebra
- Schauder fixed-point theorem
- Riesz–Markov–Kakutani representation theorem
- Perfectly normal space
- Littlewood's three principles
- FK-space
- Cauchy formula for repeated integration
- Attractor
- Optimal control
- Discontinuous additive functions via a Hamel basis
- Continuous function with divergent Fourier series
- de Rham curve
- Well-posed problem
- Bohr's approximation theorem
- Lusin's theorem
- Universal approximation theorem
- Chebyshev system
- Schauder fixed-point theorem for integral equations
- Local trivialization
- Weak convergence of measures
- Density of trigonometric polynomials in continuous functions
- Linear integral equation
- Partition of unity
- Koebe's theorem on the mean value property
- Spline
- Bohr almost periodic function
- Bernstein–Doetsch theorem
- Integral equation of the third kind
- Minimax approximation
- Poisson integral formula
- Butterfly effect
- Hahn–Mazurkiewicz theorem
- Space-filling curve
- Galois representation
- Linking number
- Dirichlet's principle
- Mean-periodic function
- Lebesgue constants of the Dirichlet kernel
- Suspension flow
- Remez algorithm
- Scott continuity
- Bifurcation in a family of maps
- BK-space
- Nyström method
- Kolmogorov–Arnold representation theorem
- Hilbert's thirteenth problem
- Poisson integral for the half-space
- Harmonic space
- Schwarz reflection principle for harmonic functions
- Almost periodic function
- Sierpiński's theorem on measurable midpoint convex functions
- Approximation by convolution with mollifiers
- Loewner differential equation
- Cauchy's functional equation
- Green's function
- Weighted polynomial approximation
- Faber's theorem on interpolation