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...field]], giving an algebraic generalisation of the way a [[Lattice (group)|lattice group]] is embedded in a [[real number|real]] vector space. ...''K''. An ''R''-[[submodule]] ''M'' of a ''K''-vector space ''V'' is a ''lattice'' if ''M'' is [[finitely generated module|finitely generated]] over ''R''. ...

...umb|Example valuation function on the cube lattice which makes it a metric lattice.]] ...Edwin | last = Rutherford | year = 1965 | title = Introduction to Lattice Theory ...

...that has a [[partial order]] <math>\,\leq\,</math> making it into [[vector lattice]] that possesses a neighborhood base at the origin consisting of [[solid se Ordered vector lattices have important applications in [[spectral theory]]. ...

In mathematics, specifically in [[order theory]] and [[functional analysis]], a subset <math>A</math> of an [[ordered vect ...|Beckenstein|2011|pp=139-153}} in which case it is necessarily a [[vector lattice]]. ...

{{Short description|Banach space with a compatible structure of a lattice}} ...|(''X'',‖·‖)}} is a [[Banach space|complete normed vector space]] with a [[lattice order]], <math>\leq</math>, such that for all {{math|''x'', ''y'' ∈ ''X''}} ...

...e''', an '''AL-space''', or an '''abstract Lebesgue space''' is a [[Banach lattice]] <math>(X, \| \cdot \|)</math> whose norm is additive on the positive cone In [[probability theory]], it means the [[standard probability space]].<ref>{{citation |title=Stati ...

...heory]] and [[functional analysis]], a subset <math>S</math> of a [[vector lattice]] <math>X</math> is said to be '''solid''' and is called an '''ideal''' if In a [[locally convex vector lattice]] <math>X,</math> the [[polar set|polar]] of every solid neighborhood of th ...

...]], a '''locally convex vector lattice (LCVL)''' is a [[topological vector lattice]] that is also a [[locally convex]] space.{{sfn|Schaefer|Wolff|1999|pp=234– LCVLs are important in the theory of [[topological vector lattice]]s. ...

In mathematics, specifically in [[order theory]] and [[functional analysis]], an [[ordered vector space]] <math>X</math> i ...ector space is an important property in the theory of [[topological vector lattice]]s. ...

...ory]] and [[functional analysis]], an element <math>x</math> of a [[vector lattice]] <math>X</math> is called a '''weak order unit''' in <math>X</math> if <ma ...Separable space|separable]] [[Fréchet space|Fréchet]] [[topological vector lattice]] then the set of weak order units is dense in the positive cone of <math>X ...

...of lattice points in the plane has a large subset whose centroid is also a lattice point}} ...point]]s in the plane has a large [[subset]] whose [[centroid]] is also a lattice point. It was proved independently in the autumn of 2003 by [[Christian Rei ...

...heory)|filter]] <math>\mathcal{F}</math> in an [[order complete]] [[vector lattice]] <math>X</math> is '''order convergent''' if it contains an [[Order bounde Order convergence plays an important role in the theory of [[vector lattice]]s because the definition of order convergence does not depend on any topol ...

...udocomplement is unique by definition (if it exists), a pseudocomplemented lattice can be endowed with a unary operation * mapping every element to its pseudo ...ce|distributive]] ''p''-algebra, ''S''(''L'') is the set of [[Complemented lattice|complemented]] elements of ''L''.<ref name="Blyth"/> ...

...Volterra lattice is an [[integrable system]], and is related to the [[Toda lattice]]. It is also used as a model for [[Langmuir wave]]s in plasmas. The Volterra lattice is the set of ordinary differential equations for functions ''a''<sub>''n'' ...

...is finite. Also equivalent is the existence of a uniform [[tree lattice|X-lattice]] in G. [[Category:Trees (graph theory)]] ...

...lysis]], two elements ''x'' and ''y'' of a [[vector lattice]] ''X'' are '''lattice disjoint''' or simply '''disjoint''' if <math>\inf \left\{ |x|, |y| \right\ We say that two sets ''A'' and ''B'' are '''lattice disjoint''' or '''disjoint''' if ''a'' and ''b'' are disjoint for all ''a'' ...

...n [[order theory]] and [[functional analysis]], a '''band''' in a [[vector lattice]] <math>X</math> is a subspace <math>M</math> of <math>X</math> that is [[s For any subset <math>S</math> of a vector lattice <math>X,</math> the set <math>S^{\perp}</math> of all elements of <math>X</ ...

...ive transformation]]s that send the graph to itself is a [[lattice (group)|lattice in the group-theoretical sense]]. ...lane or 3D space). This type of graph may more shortly be called just a '''lattice''', '''mesh''', or '''grid'''. Moreover, these terms are also commonly used ...

{{Short description|Lattice fermion discretisation}} ...bcode=1974PhRvD..10.2445W }}</ref> They are widely used, for instance in [[lattice QCD]] calculations.<ref>{{cite book ...

...ts are named after [[Leonhard Euler]]. Eulerian lattices generalize [[face lattice]]s of [[convex polytope]]s and much recent research has been devoted to ext ...e empty face, and the largest element, the polytope itself, is an Eulerian lattice. The odd–even condition follows from [[Euler characteristic|Euler's formula ...