Compact set
Summary
A compact subset of a topological space is a subset that is a compact space with the subspace topology. Equivalently, each cover of the subset by open sets of the space has a finite subcover.
Where this leads
99 pages build on this one.
- Banach–Alaoglu theorem
- Krylov–Bogolyubov theorem
- Collectively compact operator approximation
- Ergodic decomposition
- Jung's theorem
- Fundamental theorem of Γ-convergence
- Vietoris topology
- Montel space
- Eberlein–Šmulian theorem
- Transfinite diameter
- Lyapunov's convexity theorem
- Variational capacity
- q-convex manifold
- van Dantzig's theorem
- Zeros of holomorphic functions are not isolated
- Minkowski's second theorem
- Hecke algebra of a locally compact group
- Capacitability of Borel sets
- Hahn–Banach separation theorem
- Evans potential theorem
- Double bubble theorem
- Mahler's compactness theorem
- Capacity and Hausdorff dimension
- Schaefer's fixed point theorem
- Kakutani fixed-point theorem
- Bolza problem
- Gauss variational problem
- Compact operator
- Brunn–Minkowski theorem
- Tightness of measures
- Logarithmic capacity
- Sigma-compact space
- Leray–Schauder method
- Mackey topology
- Value function
- Centerpoint theorem
- Stein space
- Capacity of a disc and a segment
- Prokhorov's theorem
- Blaschke selection theorem
- Schauder fixed-point theorem
- Supporting hyperplane theorem
- Successive minima
- Stein manifold
- Straszewicz's theorem
- Helly's theorem
- Compactness of the spectrum
- Dido's problem
- Hartogs's extension theorem
- Radon measure
- Frostman lemma
- Polynomially convex set
- Gelfand pair
- Lusin's theorem
- Equilibrium measure
- Variational principle for topological entropy
- Universal approximation theorem
- Lomonosov's invariant subspace theorem
- Schauder fixed-point theorem for integral equations
- Fractional Helly theorem
- Isoperimetric inequality
- Approximation property
- Unique ergodicity
- Viscosity solution of the Hamilton–Jacobi–Bellman equation
- Kontinuitätssatz
- Oka manifold
- Plurisubharmonic exhaustion function
- Łojasiewicz inequality
- Sets of capacity zero
- Locally finite measure
- Minkowski–Carathéodory theorem
- Choquet theory
- Ky Fan minimax inequality
- Removable sets for bounded harmonic functions
- Holomorphically convex hull
- Bang–bang control
- Krein–Milman theorem
- Relaxed control
- Inner regular measure
- Verification theorem
- Capacity of a set
- Proper map
- Frostman's theorem
- Capacity equals transfinite diameter and Chebyshev constant
- Compact-open topology
- Fekete points
- Brunn–Minkowski theory
- Condenser capacity
- Filippov's existence theorem
- Almost periodic function
- Kirchberger's theorem
- Pseudoconvexity
- Chebyshev constant
- Robin constant
- Convex body
- Colombeau algebra
- Hartogs lemma for subharmonic functions
- Holomorphically convex domain
- Support of a convolution
Further reading
- Web https://en.wikipedia.org/wiki/Compact_space, Compactness of subsets
About this page
| Tag | 0R6EWFKRCF |
|---|---|
| URI | m2://0R6EWFKRCF |
| Aliases | compact-subset |
| Kind | concept |
| Writing | W0 stub |
| MSC | 54D30 |
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Definitions
Used by
- Banach–Alaoglu theorem
- Collectively compact operator approximation
- Fundamental theorem of Γ-convergence
- Vietoris topology
- Montel space
- Eberlein–Šmulian theorem
- Transfinite diameter
- Lyapunov's convexity theorem
- Variational capacity
- q-convex manifold
- van Dantzig's theorem
- Minkowski's second theorem
- Hecke algebra of a locally compact group
- Capacitability of Borel sets
- Hahn–Banach separation theorem
- Evans potential theorem
- Mahler's compactness theorem
- Capacity and Hausdorff dimension
- Kakutani fixed-point theorem
- Gauss variational problem
- Compact operator
- Brunn–Minkowski theorem
- Tightness of measures
- Logarithmic capacity
- Sigma-compact space
- Leray–Schauder method
- Mackey topology
- Value function
- Stein space
- Prokhorov's theorem
- Blaschke selection theorem
- Schauder fixed-point theorem
- Successive minima
- Stein manifold
- Straszewicz's theorem
- Helly's theorem
- Compactness of the spectrum
- Hartogs's extension theorem
- Radon measure
- Frostman lemma
- Polynomially convex set
- Gelfand pair
- Lusin's theorem
- Equilibrium measure
- Universal approximation theorem
- Approximation property
- Viscosity solution of the Hamilton–Jacobi–Bellman equation
- Kontinuitätssatz
- Oka manifold
- Plurisubharmonic exhaustion function
- Łojasiewicz inequality
- Sets of capacity zero
- Locally finite measure
- Minkowski–Carathéodory theorem
- Choquet theory
- Ky Fan minimax inequality
- Removable sets for bounded harmonic functions
- Holomorphically convex hull
- Bang–bang control
- Krein–Milman theorem
- Relaxed control
- Inner regular measure
- Capacity of a set
- Proper map
- Frostman's theorem
- Capacity equals transfinite diameter and Chebyshev constant
- Compact-open topology
- Fekete points
- Condenser capacity
- Filippov's existence theorem
- Almost periodic function
- Pseudoconvexity
- Chebyshev constant
- Robin constant
- Convex body
- Colombeau algebra
- Hartogs lemma for subharmonic functions
- Holomorphically convex domain
- Support of a convolution