General topology Basic notions: open sets, neighbourhoods, bases Concept
Open set
Summary
An open set is a member of a topology. In a metric space, a set is open when each of its points has a small ball around it that stays in the set.
Where this leads
146 pages build on this one.
- Completely normal space
- Relative CW complex
- Holomorphic map
- Locally path-connected space
- Vietoris topology
- Phragmén–Lindelöf principle for subharmonic functions
- Holomorphic function of several variables
- Lakes of Wada
- Regular boundary point
- Superharmonic function
- Pointless topology
- Kolmogorov quotient
- Beltrami equation
- Open subgroup
- Rational map
- Portmanteau theorem
- Particular point topology
- Harmonic at a point
- Hyperfunction
- Hartogs domain
- Zeros of holomorphic functions are not isolated
- Quasi-projective variety
- Hyperconnected space
- Levi form
- Riemann extension theorem in several variables
- Neumann problem
- Locale
- Domain of holomorphy
- Harmonic majorant
- Frame
- Banach bundle
- Invariance of domain
- Absolute neighborhood retract
- Local homeomorphism
- Sheaf
- Log-modulus of a holomorphic function is subharmonic
- Barrier
- Single layer potential
- Reduced function
- Regular open set
- G-delta set
- Excluded point topology
- Clopen set
- Final topology
- Positive harmonic function
- Maximum principle for subharmonic functions
- Subharmonic function
- Poisson's equation
- Disjoint union topology
- Almgren–Pitts min-max theory
- Quasiconformal mapping
- Dirichlet energy
- Edge-of-the-wedge theorem
- Monad in nonstandard topology
- Exterior cone condition
- Varadhan's lemma
- Fréchet manifold
- Heyting algebra
- Sub-mean value property
- Riesz decomposition theorem
- Lipschitz domain
- Alexandrov topology
- Hemicontinuity
- Extremally disconnected space
- Topological transitivity
- Locally connected space
- Topology of pointwise convergence
- Presheaf
- Perfectly normal space
- Regular function
- Convex functions of subharmonic functions
- Lebesgue spine
- Superharmonic potential
- Integral functional with a Lagrangian density
- Resolutivity of boundary functions
- Attractor
- Stalk
- Riesz measure of a subharmonic function
- Hartogs's extension theorem
- Fredholm map
- Sequential space
- Double layer potential
- Outer regular measure
- Symmetry of the Green function
- Carathéodory's criterion
- Fundamental lemma of the calculus of variations
- Open embedding theorem for Hilbert manifolds
- Wandering set
- Large deviations theory
- Perron method
- Runge domain
- Locally finite measure
- Piecewise linear manifold
- Polyharmonic function
- Topological mixing
- Sierpiński space
- Kelvin transform
- Hilbert manifold
- Quasicircle
- Littlewood subordination theorem
- Partial differential equation
- Atlas
- Least harmonic majorant
- Domain of finite type
- Sanov's theorem
- Holomorphically convex hull
- Fatou set
- Fundamental convergence theorem
- Dirichlet's principle
- Baire property
- Cramér's theorem
- Residuated lattice
- Wiener's criterion
- Inductive dimension
- Alexander–Spanier cohomology
- Analytic continuation in several variables
- Hadamard three-circle theorem for subharmonic functions
- Lindelöf's maximum principle
- Meromorphic function of several variables
- Measurable Riemann mapping theorem
- Compact-open topology
- Banach–Lie group
- Perron–Wiener–Brelot solution
- Banach manifold
- Thom–Mather stratified space
- Reinhardt domain
- Function field of a variety
- Kellogg–Evans theorem
- Tube lemma
- Morphism of varieties
- Geometric realization
- Schwarz reflection principle for harmonic functions
- Pseudoconvexity
- Bochner's tube theorem
- Manifold with boundary
- Semicontinuity
- Current
- Topological manifold
- Varifold
- Birational map
- Colombeau algebra
- Support of a measure
- Method of images
- Hartogs lemma for subharmonic functions
- Holomorphically convex domain
- Open immersion
Further reading
- Web https://en.wikipedia.org/wiki/Open_set, lead section
About this page
| Tag | 02BH3MCBQB |
|---|---|
| URI | m2://02BH3MCBQB |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54A05 |
| Same as |
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What links here
Definitions
Used by
- Completely normal space
- Holomorphic map
- Locally path-connected space
- Vietoris topology
- Holomorphic function of several variables
- Lakes of Wada
- Regular boundary point
- Superharmonic function
- Pointless topology
- Kolmogorov quotient
- Beltrami equation
- Open subgroup
- Rational map
- Portmanteau theorem
- Particular point topology
- Harmonic at a point
- Hyperfunction
- Hartogs domain
- Quasi-projective variety
- Hyperconnected space
- Levi form
- Riemann extension theorem in several variables
- Neumann problem
- Locale
- Domain of holomorphy
- Harmonic majorant
- Frame
- Invariance of domain
- Absolute neighborhood retract
- Local homeomorphism
- Sheaf
- Log-modulus of a holomorphic function is subharmonic
- Barrier
- Single layer potential
- Reduced function
- Regular open set
- G-delta set
- Excluded point topology
- Clopen set
- Final topology
- Positive harmonic function
- Maximum principle for subharmonic functions
- Subharmonic function
- Poisson's equation
- Disjoint union topology
- Quasiconformal mapping
- Dirichlet energy
- Edge-of-the-wedge theorem
- Monad in nonstandard topology
- Exterior cone condition
- Fréchet manifold
- Heyting algebra
- Riesz decomposition theorem
- Lipschitz domain
- Alexandrov topology
- Hemicontinuity
- Extremally disconnected space
- Topological transitivity
- Locally connected space
- Topology of pointwise convergence
- Presheaf
- Perfectly normal space
- Regular function
- Convex functions of subharmonic functions
- Superharmonic potential
- Integral functional with a Lagrangian density
- Resolutivity of boundary functions
- Attractor
- Stalk
- Riesz measure of a subharmonic function
- Hartogs's extension theorem
- Sequential space
- Double layer potential
- Outer regular measure
- Symmetry of the Green function
- Carathéodory's criterion
- Fundamental lemma of the calculus of variations
- Open embedding theorem for Hilbert manifolds
- Wandering set
- Large deviations theory
- Perron method
- Runge domain
- Locally finite measure
- Piecewise linear manifold
- Polyharmonic function
- Topological mixing
- Sierpiński space
- Kelvin transform
- Partial differential equation
- Atlas
- Least harmonic majorant
- Holomorphically convex hull
- Fatou set
- Fundamental convergence theorem
- Dirichlet's principle
- Baire property
- Wiener's criterion
- Inductive dimension
- Alexander–Spanier cohomology
- Analytic continuation in several variables
- Meromorphic function of several variables
- Compact-open topology
- Perron–Wiener–Brelot solution
- Banach manifold
- Thom–Mather stratified space
- Reinhardt domain
- Function field of a variety
- Kellogg–Evans theorem
- Tube lemma
- Morphism of varieties
- Schwarz reflection principle for harmonic functions
- Pseudoconvexity
- Bochner's tube theorem
- Manifold with boundary
- Semicontinuity
- Current
- Topological manifold
- Varifold
- Birational map
- Colombeau algebra
- Support of a measure
- Method of images
- Hartogs lemma for subharmonic functions
- Holomorphically convex domain
- Open immersion