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1 revision imported from alpha:Template:Topological_vector_spaces

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alpha>Sarika: Created page with "{{Navbox | name = Topological vector spaces | title = Topological vector spaces (TVSs) | state = {{{state|uncollapsed autocollapse expanded
2022-12-06T10:20:07Z

Created page with "{{Navbox | name = Topological vector spaces | title = Topological vector spaces (TVSs) | state = {{{state|<noinclude>uncollapsed autocollapse expanded</noinclude><includeo..."

← Older revision Revision as of 15:50, 6 December 2022
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wikipedia>Mgkrupa at 01:13, 11 May 2022

2022-05-11T01:13:33Z

New page

{{Navbox
| name = Topological vector spaces
| title = [[Topological vector space]]s (TVSs)
| state = {{{state|<noinclude>uncollapsed autocollapse expanded</noinclude><includeonly>autocollapse</includeonly>}}}

| image =
| bodyclass = hlist
| selected = {{{1}}}
| above =

| group1 = Basic concepts
| list1 =
* [[Banach space]]
* [[Metrizable topological vector space|Completeness]]
* [[Continuous linear operator]]
* [[Linear form|Linear functional]]
* [[Fréchet space]]
* [[Linear map]]
* [[Locally convex topological vector space|Locally convex space]]
* [[Metrizable topological vector space|Metrizability]]
* [[Operator topologies]]
* [[Topological vector space]]
* [[Vector space]]

| group5 = [[:Category:Theorems in functional analysis|Main results]]
| list5 =
* [[Anderson–Kadec theorem|Anderson–Kadec]]
* [[Banach–Alaoglu theorem|Banach–Alaoglu]]
* [[Closed graph theorem (functional analysis)|Closed graph theorem]]
* [[F. Riesz's theorem|F. Riesz's]]
* [[Hahn–Banach theorem|Hahn–Banach]] ([[Hyperplane separation theorem|hyperplane separation]]
* [[Vector-valued Hahn–Banach theorems|Vector-valued Hahn–Banach]])
* [[Open mapping theorem (functional analysis)|Open mapping (Banach–Schauder)]]
** [[Bounded inverse theorem|Bounded inverse]]
* [[Uniform boundedness principle|Uniform boundedness (Banach–Steinhaus)]]

| group10 = Maps
| list10 =
* [[Bilinear operator]]
** [[Bilinear form|form]]
* [[Linear map]]
** [[Almost open linear map|Almost open]]
** [[Bounded operator|Bounded]]
** [[Continuous linear operator|Continuous]]
** [[Closed linear operator|Closed]]
** [[Compact operator|Compact]]
** [[Densely defined operator|Densely defined]]
** [[Discontinuous linear map|Discontinuous]]
* [[Topological homomorphism]]
* [[Functional (mathematics)|Functional]]
** [[Linear form|Linear]]
** [[Bilinear form|Bilinear]]
** [[Sesquilinear form|Sesquilinear]]
* [[Norm (mathematics)|Norm]]
* [[Seminorm]]
* [[Sublinear function]]
* [[Transpose of a linear map|Transpose]]

| group15 = Types of sets
| list15 =
* [[Absolutely convex set|Absolutely convex/disk]]
* [[Absorbing set|Absorbing/Radial]]
* [[Affine space|Affine]]
* [[Balanced set|Balanced/Circled]]
* [[Auxiliary normed space|Banach disks]]
* [[Bounding point]]s
* [[Bounded set (topological vector space)|Bounded]]
* [[Complemented subspace]]
* [[Convex set|Convex]]
* [[Convex cone|Convex cone {{smaller|(subset)}}]]
* [[Cone (linear algebra)|Linear cone {{smaller|(subset)}}]]
* [[Extreme point]]
* [[Totally bounded space#Topological vector spaces|Pre-compact/Totally bounded]]
* [[Prevalent and shy sets|Prevalent/Shy]]
* [[Radial set|Radial]]
* [[Star domain|Radially convex/Star-shaped]]
* [[Symmetric set|Symmetric]]

| group20 = Set operations
| list20 =
* [[Affine hull]]
* ([[Algebraic interior#Relative algebraic interior|Relative]]) [[Algebraic interior|Algebraic interior (core)]]
* [[Convex hull]]
* [[Linear span]]
* [[Minkowski addition|Minkowski addition]]
* [[Polar set|Polar]]
* ([[Algebraic interior#Quasi relative interior|Quasi]]) [[Algebraic interior#Relative interior|Relative interior]]

| group40 = Types of TVSs
| list40 =
* [[Asplund space|Asplund]]
* [[Ptak space|B-complete/Ptak]]
* [[Banach space|Banach]]
* ([[Countably barrelled space|Countably]]) [[Barrelled space|Barrelled]]
* [[BK-space]]
* ([[Ultrabornological space|Ultra-]]) [[Bornological space|Bornological]]
* [[Brauner space|Brauner]]
* [[Complete topological vector space|Complete]]
* [[Convenient vector space|Convenient]]
* [[DF-space|(DF)-space]]
* [[Distinguished space|Distinguished]]
* [[F-space]]
* [[FK-AK space]]
* [[FK-space]]
* [[Fréchet space|Fréchet]]
** [[Differentiation in Fréchet spaces#Tame Fréchet spaces|tame Fréchet]]
* [[Grothendieck space|Grothendieck]]
* [[Hilbert space|Hilbert]]
* [[Infrabarreled space|Infrabarreled]]
* [[Interpolation space]]
* [[K-space (functional analysis)|K-space]]
* [[LB-space]]
* [[LF-space]]
* [[Locally convex topological vector space|Locally convex space]]
* [[Mackey space|Mackey]]
* [[Metrizable topological vector space|(Pseudo)Metrizable]]
* [[Montel space|Montel]]
* [[Quasibarrelled space|Quasibarrelled]]
* [[Quasi-complete]]
* [[Quasinorm|Quasinormed]]
* ([[Polynomially reflexive space|Polynomially]]
* [[Semi-reflexive space|Semi-]]) [[Reflexive space|Reflexive]]
* [[Riesz space|Riesz]]
* [[Schwartz TVS|Schwartz]]
* [[Semi-complete]]
* [[Smith space|Smith]]
* [[Stereotype space|Stereotype]]
* ([[B-convex space|B]]
* [[Strictly convex space|Strictly]]
* [[Uniformly convex space|Uniformly]]) convex
* ([[Quasi-ultrabarrelled space|Quasi-]]) [[Ultrabarrelled space|Ultrabarrelled]]
* [[Uniformly smooth space|Uniformly smooth]]
* [[Webbed space|Webbed]]
* [[Approximation property|With the approximation property]]

}}<noinclude>
{{Documentation
| content =
{{Collapsible option |statename=optional}}
}}
[[Category:Mathematics navigational boxes]]
[[Category:Topological vector spaces]]
</noinclude>

← Older revision	Revision as of 15:50, 6 December 2022
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Template:Topological vector spaces - Revision history

Indicwiki: 1 revision imported from :alpha:Template:Topological_vector_spaces

Admin: 1 revision imported

wikipedia>Mgkrupa at 01:13, 11 May 2022