About: Locally convex vector lattice

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In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in the theory of topological vector lattices.

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rdfs:label	Locally convex vector lattice (en)
rdfs:comment	In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in the theory of topological vector lattices. (en)
name	Theorem (en) Corollary (en)
dct:subject	Functional analysis
Wikipage page ID	63990620 (xsd:integer)
Wikipage revision ID	1119697200 (xsd:integer)
Link from a Wikipage to another Wikipage	Bornological space Convex set Order theory Separable space Quasi-interior point Minkowski functional Order complete Order dual (functional analysis) Ordered topological vector space Fréchet lattice Functional analysis Mackey topology Balanced set Banach lattice Normed lattice Absorbing set Functional analysis Infrabarreled Metrizable topological vector space Order convergent Order topology (functional analysis) Reflexive space Semi-reflexive Locally convex Sequentially complete Solid set Topological vector lattice Barreled space Minimal vector lattice Majorized Semi-norm dbr:Locally_convex__topological_vectore_space dbr:Regular_order_(mathematics)
sameAs	Locally convex vector lattice Locally convex vector lattice
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Reflist dbt:Sfn dbt:Functional_analysis dbt:Math_theorem dbt:Narici_Beckenstein_Topological_Vector_Spaces dbt:Ordered_topological_vector_spaces dbt:Schaefer_Wolff_Topological_Vector_Spaces
has abstract	In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in the theory of topological vector lattices. (en)
math statement	Suppose that is an order complete locally convex vector lattice with topology and endow the bidual of with its natural topology and canonical order . The following are equivalent: The evaluation map induces an isomorphism of with an order complete sublattice of For every majorized and directed subset of the section filter of converges in . Every order convergent filter in converges in . (en) Let be an order complete vector lattice with a regular order. The following are equivalent: is of minimal type. For every majorized and direct subset of the section filter of converges in when is endowed with the order topology. Every order convergent filter in converges in when is endowed with the order topology. Moreover, if is of minimal type then the order topology on is the finest locally convex topology on for which every order convergent filter converges. (en)
prov:wasDerivedFrom	wikipedia-en:Locally_convex_vector_lattice?oldid=1119697200&ns=0
page length (characters) of wiki page	6875 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Locally_convex_vector_lattice
is Link from a Wikipage to another Wikipage of	Order dual (functional analysis) Fréchet lattice Lattice disjoint Order topology (functional analysis) Solid set Normed vector lattice Lattice semi-norm Locally convex lattice
is Wikipage redirect of	Lattice semi-norm Locally convex lattice
is foaf:primaryTopic of	wikipedia-en:Locally_convex_vector_lattice

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