Properties (69)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
neighborhood
|
| gptkbp:field |
Can be infinite-dimensional.
|
| gptkbp:hasArea |
A countable basis may not exist.
|
| gptkbp:hasExhibition |
The space of continuous functions on a compact interval.
The space of analytic functions. The space of bounded continuous functions. The space of differentiable functions. The space of rapidly decreasing functions. The space of smooth functions. The space of test functions. |
| gptkbp:hasRelatedPatent |
Signal_Processing.
|
| gptkbp:hasSpecialty |
Every Cauchy sequence converges.
|
| https://www.w3.org/2000/01/rdf-schema#label |
Frechet Space
|
| gptkbp:isAvenueFor |
Differential Equations.
|
| gptkbp:isCharacterizedBy |
The convergence of sequences is defined in terms of seminorms.
A family of seminorms. A translation-invariant metric. Completeness and local convexity. The convergence of nets. The existence of a countable family of seminorms. The topology is defined by a family of seminorms. The topology is generated by seminorms. A topology that is finer than the topology induced by any seminorm. |
| gptkbp:isCitedBy |
A complete locally convex space.
A topology generated by a family of seminorms. A complete metric space with a translation-invariant metric. A structure that allows for the study of functional convergence. A metric space that is complete and locally convex. A topology that allows for the study of convergence. A_structure_that_generalizes_Banach_spaces. |
| gptkbp:isConnectedTo |
Topology.
Functional Analysis. Real Analysis. Analysis. Measure Theory. Functional_Spaces. Topological_Vector_Space. |
| gptkbp:isNamedAfter |
Maurice_Fréchet.
|
| gptkbp:isPartOf |
Functional Analysis.
Abstract Algebra. Modern Analysis. The study of infinite-dimensional spaces. Theoretical Mathematics. Advanced_Mathematics. |
| gptkbp:isRelatedTo |
Banach Space
Weak Convergence. Functional_Spaces. Locally_Convex_Space. Metric_Spaces. Normed_Spaces. Sobolev_Spaces. Topological_Groups. |
| gptkbp:isSimilarTo |
Hilbert_Space.
|
| gptkbp:isStudiedIn |
Mathematics.
|
| gptkbp:isUsedFor |
Studying convergence of sequences.
|
| gptkbp:isUsedIn |
Functional Analysis
Approximation Theory. Optimization Problems. Mathematical_Logic. Mathematical_Physics. Quantum_Mechanics. Theoretical_Computer_Science. |
| gptkbp:isUtilizedIn |
Differential Geometry.
Functional Equations. Numerical Analysis. Theoretical_Physics. Mathematical_Modeling. Control_Theory. Statistical_Mechanics. |