About: Complete topological vector space

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Complete topological vector space Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FComplete_topological_vector_space

In functional analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively closer to each other, then there exists some point towards which they all get closer. The notion of "points that get progressively closer" is made rigorous by Cauchy nets or Cauchy filters, which are generalizations of Cauchy sequences, while "point towards which they all get closer" means that this Cauchy net or filter converges to The notion of completeness for TVSs uses the theory of uniform spaces as a framework to generalize the notion of completeness for metric spaces. But unlike metric-completeness, TVS-completeness does not depend on any metric and is defined for all TVSs, including those that ar

Attributes	Values
rdf:type	Thing
rdfs:label	Complete topological vector space (en)
rdfs:comment	In functional analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively closer to each other, then there exists some point towards which they all get closer. The notion of "points that get progressively closer" is made rigorous by Cauchy nets or Cauchy filters, which are generalizations of Cauchy sequences, while "point towards which they all get closer" means that this Cauchy net or filter converges to The notion of completeness for TVSs uses the theory of uniform spaces as a framework to generalize the notion of completeness for metric spaces. But unlike metric-completeness, TVS-completeness does not depend on any metric and is defined for all TVSs, including those that ar (en)
rdfs:seeAlso	Topological group Topology Filters Net (mathematics) Topological space Completion (uniform space)
name	Theorem (en) Corollary (en) Properties of Hausdorff completions (en)
dcterms:subject	Topological vector spaces Uniform spaces Functional analysis
Wikipage page ID	53695856 (xsd:integer)
Wikipage revision ID	1124136590 (xsd:integer)
Link from a Wikipage to another Wikipage	Preorder Projective tensor product Quasi-complete Schwartz space Metrizable space Convergent filter Convergent net Convergent prefilter Topological complement Barrelled space Bornological space Bounded set (topological vector space) Topological vector spaces Relatively compact DF-space Uniform space LB-space Compact space Complemented subspace Complete TVS Complete uniformity Continuous dual space Mathematics Norm (mathematics) Nuclear space Separable space Quasi-complete space Equicontinuity Equicontinuous Fréchet space Convex combination Locally convex topological vector space Lp-space Lp space Uniform spaces Complete metric space Dense set Functional analysis Orthonormal basis Mackey space Totally bounded space Balanced set Banach space Topological group Topological homomorphism Topological vector space Topological vector spaces Topologies on spaces of linear maps Topology (structure) Total order Totally bounded Weak-* topology Distributive property Hausdorff space Linear map Locally compact space Absolutely convex set Dual system F-space Filter (set theory) Filters in topology Normed space Partial sum Cauchy sequence Directed set Family of sets Pseudometric space Quotient space (linear algebra) Quotient space (topology) Hilbert space Isometric isomorphism Baire space First-countable Functional analysis LF-space Lebesgue integration Topological tensor product Trivial topology Diameter Differentiable vector-valued functions from Euclidean space Distribution (mathematics) Polar topology Spaces of test functions and distributions

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 60 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software