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Statements

Subject Item
dbr:Locally_convex_vector_lattice
rdfs:label
Locally convex vector lattice
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.
dbp:name
Theorem Corollary
dct:subject
dbc:Functional_analysis
dbo:wikiPageID
63990620
dbo:wikiPageRevisionID
1119697200
dbo:wikiPageWikiLink
dbc:Functional_analysis dbr:Reflexive_space dbr:Mackey_topology dbr:Order_convergent dbr:Semi-reflexive dbr:Order_dual_(functional_analysis) dbr:Solid_set dbr:Order_complete dbr:Banach_lattice dbr:Bornological_space dbr:Infrabarreled dbr:Functional_analysis dbr:Majorized dbr:Order_theory dbr:Ordered_topological_vector_space dbr:Locally_convex__topological_vectore_space dbr:Minimal_vector_lattice dbr:Absorbing_set dbr:Regular_order_(mathematics) dbr:Fréchet_lattice dbr:Minkowski_functional dbr:Balanced_set dbr:Locally_convex dbr:Semi-norm dbr:Convex_set dbr:Separable_space dbr:Topological_vector_lattice dbr:Sequentially_complete dbr:Quasi-interior_point dbr:Metrizable_topological_vector_space dbr:Order_topology_(functional_analysis) dbr:Barreled_space dbr:Normed_lattice
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dbt:Reflist dbt:Annotated_link dbt:Narici_Beckenstein_Topological_Vector_Spaces dbt:Functional_analysis dbt:Sfn dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Math_theorem dbt:Ordered_topological_vector_spaces
dbo: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.
dbp:mathStatement
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. 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 .
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wikipedia-en:Locally_convex_vector_lattice?oldid=1119697200&ns=0
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6875
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wikipedia-en:Locally_convex_vector_lattice