Convex space information

mathematics, a convex space (or barycentric algebra) is a space in which it is possible to take convex combinations of any sets of points. A convex space can be...

locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They...

In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset...

In mathematics, uniformly convex spaces (or uniformly rotund spaces) are common examples of reflexive Banach spaces. The concept of uniform convexity...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

strictly convex space is a normed vector space (X, || ||) for which the closed unit ball is a strictly convex set. Put another way, a strictly convex space is...

locally convex. Banach spaces, Hilbert spaces and Sobolev spaces are other well-known examples of TVSs. Many topological vector spaces are spaces of functions...

mathematics known as functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from X {\displaystyle...

subset of a vector space that is closed under linear combinations with positive coefficients. It follows that convex cones are convex sets. In this article...

… , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} in a real vector space, a convex combination of these points is a point of the form α 1 x 1 + α 2 x...

n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} . Most texts use the term "polytope" for a bounded convex polytope, and the word "polyhedron"...

spaces Locally convex topological vector space – a vector space with a topology defined by convex open sets Space (mathematics) – mathematical set with some...

a subcontractor f is compact, then f has a fixed point. In a locally convex space (E, P) with topology given by a set P of seminorms, one can define for...

Fréchet space – A locally convex topological vector space that is also a complete metric space Hardy space – Concept within complex analysis Hilbert space –...

or a barrel in a topological vector space is a set that is convex, balanced, absorbing, and closed. Barrelled spaces are studied because a form of the Banach–Steinhaus...

a bornological space into any locally convex spaces is continuous if and only if it is a bounded linear operator. Bornological spaces were first studied...

convex set of points Strictly convex set, a set whose interior contains the line between any two points Strictly convex space, a normed vector space for...

In mathematics, convex metric spaces are, intuitively, metric spaces with the property any "segment" joining two points in that space has other points...

{\displaystyle X} is nuclear if for every locally convex space Y , {\displaystyle Y,} the canonical vector space embedding X ⊗ π Y → B ε ( X σ ′ , Y σ ′ ) {\displaystyle...

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 metrizable...

topological vector spaces; it dates to a 1935 paper of John von Neumann. This definition has the appealing property that, in a locally convex space endowed with...

analysis, a seminorm is a vector space norm that need not be positive definite. Seminorms are intimately connected with convex sets: every seminorm is the...

X} is a locally convex space, the strong topology on the (continuous) dual space X ′ {\displaystyle X^{\prime }} (that is, on the space of all continuous...

In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the...