topological vector space

GPTKB entity

Statements (27)
Predicate Object
gptkbp:instanceOf gptkb:Vector
gptkb:algebra
gptkb:topology
gptkbp:category gptkb:Topological_vector_spaces
gptkbp:field complex numbers
real numbers
gptkbp:generalizes gptkb:Hilbert_space
gptkb:normed_vector_space
gptkb:Fréchet_space
locally convex space
metrizable topological vector space
gptkbp:hasApplication gptkb:probability_theory
partial differential equations
quantum mechanics
distribution theory
gptkbp:hasProperty Hausdorff property (optional)
open sets define topology
scalar multiplication is continuous
vector addition is continuous
zero vector is unique
gptkbp:hasWikipediaPage https://en.wikipedia.org/wiki/Topological_vector_space
gptkbp:introduced gptkb:John_von_Neumann
gptkb:Andrey_Kolmogorov
1930s
gptkbp:studiedBy functional analysis
gptkbp:bfsParent gptkb:Hilbert_space
gptkbp:bfsLayer 4