Statements (96)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
vector space with a topology such that vector addition and scalar multiplication are continuous
|
| gptkbp:example |
gptkb:Euclidean_space
gptkb:Schwartz_space gptkb:Lp_spaces gptkb:Sobolev_space space of continuous functions function spaces dual space sequence spaces space of distributions |
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:generalizes |
gptkb:Banach_spaces
gptkb:Hilbert_spaces gptkb:Fréchet_spaces normed vector spaces locally convex spaces metrizable vector spaces |
| gptkbp:hasSubfield |
gptkb:topology
functional analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Topological vector spaces
|
| gptkbp:introduced |
gptkb:John_von_Neumann
|
| gptkbp:operator |
gptkb:Baire_category_theorem
gptkb:Banach–Steinhaus_theorem gptkb:Hahn–Banach_theorem gptkb:Hilbert_space gptkb:neighborhood gptkb:Fréchet_space gptkb:Mackey_topology gptkb:Alaoglu's_theorem gptkb:Montel_space gptkb:Uniform_boundedness_principle gptkb:closed_graph_theorem gptkb:open_mapping_theorem gptkb:pre-Banach_space gptkb:pre-Hilbert_space net bounded linear operator compactness completion convergence convex set locally convex space normed space tensor product barrel continuous map metrizable space quotient space subspace topology filter absorbing set balanced set barrelled space bornological space bounded set closed graph continuous linear functional continuous linear map continuous norm continuous seminorm direct sum dual pair final topology inductive limit inductive topology initial topology nuclear space open mapping paracompact space polar set product space projective limit projective topology quasi-complete space quotient topology reflexive space seminorm seminormed space strong topology topological dual weak topology |
| gptkbp:property |
gptkb:Montel
gptkb:Hausdorff nuclear complete barrelled bornological locally convex paracompact quasi-complete reflexive separable |
| gptkbp:studiedIn |
analysis
|
| gptkbp:bfsParent |
gptkb:topological_vector_space
|
| gptkbp:bfsLayer |
5
|