areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize...

and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important...

Topological vector lattice Locally convex vector lattice Vector lattice – Partially ordered vector space, ordered as a latticePages displaying short descriptions...

categories of TVSs are locally convex topological vector spaces. This article focuses on TVSs that are not necessarily locally convex. Other well-known examples...

a lattice Complemented lattice – Bound lattice in which every element has a complement Fréchet lattice – Topological vector lattice Locally convex vector...

(X,\tau )} is a locally convex vector lattice, x {\displaystyle x} is a quasi-interior point of its positive cone. An ordered vector space X {\displaystyle...

Fréchet space X {\displaystyle X} is defined to be a locally convex metrizable topological vector space (TVS) that is complete as a TVS, meaning that every...

lattices. Every Fréchet lattice is a locally convex vector lattice. The set of all weak order units of a separable Fréchet lattice is a dense subset of its...

collection of convex sets is itself convex, so the convex subsets of a (real or complex) vector space form a complete lattice. In a real vector-space, the...

lattice (the absolute value of the determinant of any of its bases). Suppose that L is a lattice of determinant d(L) in the n-dimensional real vector...

topological vector space is locally convex if and only if its topology is induced by a family of seminorms. Let X {\displaystyle X} be a vector space over...

with convex sets of geometry, one uses order-convex instead of "convex". A convex sublattice of a lattice L is a sublattice of L that is also a convex set...

generally in a locally convex topological vector space) is the convex hull of its extreme points. However, this may not be true for convex sets that are...

topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). An LM-space is an inductive limit of a sequence of locally convex...

as in the case of the lattice (N, |), i.e., the non-negative integers ordered by divisibility. In this locally finite lattice, the infimal element denoted...

{\displaystyle ({\mathcal {F}},\subseteq ).} Locally convex vector lattice Grätzer, George (21 November 2002). General Lattice Theory: Second edition. Springer Science...

vector space, ordered as a lattice Topological vector lattice Vector lattice – Partially ordered vector space, ordered as a latticePages displaying short descriptions...

Hausdorff locally convex TVS topology on X. Generalised metric – Metric geometry Order topology (functional analysis) – Topology of an ordered vector space...

A distributive lattice is complemented if and only if it is bounded and relatively complemented. The lattice of subspaces of a vector space provide an...

algebra if and only if n is square-free. A lattice-ordered vector space is a distributive lattice. Young's lattice given by the inclusion ordering of Young...

Distortion problem Interpolation space Locally convex topological vector space – Vector space with a topology defined by convex open sets Modulus and characteristic...

various restrictions on f-vectors of convex simplicial polytopes, to this more general setting. The face lattice of a convex polytope, consisting of its...

Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces...

≤ x − 1 {\displaystyle x^{-}\leq x^{-1}} . Solid set Locally convex vector lattice Vector lattice Schaefer & Wolff 1999, pp. 204–214. Schaefer & Wolff...

bands in a vector lattice X {\displaystyle X} is a band in X . {\displaystyle X.} Solid set Locally convex vector lattice Vector lattice – Partially...

of functionals with domain a vector space and the space of functionals on the dual vector space. If V is locally convex but not Hausdorff, the kernel...

Banach lattice – Banach space with a compatible structure of a lattice Fréchet lattice – Topological vector lattice Locally convex vector lattice Vector lattice –...

{\displaystyle X} is contained in a unique smallest ideal. In a locally convex vector lattice X , {\displaystyle X,} the polar of every solid neighborhood...

Lattice Theory. Colloquium Publications. Vol. 25. Providence: Am. Math. Soc. Davey, Brian A.; Priestley, Hilary Ann (1990). Introduction to Lattices and...

Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves...