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

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. Other well-known examples of TVSs include Banach spaces, Hilbert spaces and Sobolev spaces. Many topological vector spaces are spaces of functions...

for uniformly convex Banach spaces. It asserts that if K {\displaystyle K} is a nonempty convex closed bounded set in uniformly convex Banach space and...

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

geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral...

the Lp-spaces are uniformly smooth (and uniformly convex). Enflo proved that the class of Banach spaces that admit an equivalent uniformly convex norm coincides...

( t ) . {\displaystyle n(t).} Uniformly convex spaces are super-reflexive. Let X {\displaystyle X} be uniformly convex, with modulus of convexity δ X...

Under relatively general conditions (the space is a possibly infinite-dimensional uniformly convex space, there can be infinitely many sites of a general...

on uniformly convex spaces, J. London Math. Soc. 34 (1959), 92. Day, Mahlon M. (1941). "Reflexive Banach spaces not isomorphic to uniformly convex spaces"...

spaces Banach bundle Distortion problem Interpolation space Locally convex topological vector space – Vector space with a topology defined by convex open...

compact. The uniformly continuous image of a precompact set is precompact. Although the notion of total boundedness is closely tied to metric spaces, the greater...

Hilbert space is a uniformly convex Banach space. This subsection employs the Hilbert projection theorem. If C is a non-empty closed convex subset of...

"how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ε-δ definition of uniform convexity...

Banach space is B-convex if and only if every sequence of independent, symmetric, uniformly bounded and Radon random variables in that space satisfies...

typically not Banach spaces. A Fréchet space X {\displaystyle X} is defined to be a locally convex metrizable topological vector space (TVS) that is complete...

This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight...

r} is compact. The function f has a unique global minimum on Rn. A uniformly convex function, with modulus ϕ {\displaystyle \phi } , is a function f {\displaystyle...

t_{3}B_{3},\ldots } are uniformly bounded. In words, given any countable family of bounded sets in a metrizable locally convex space, it is possible to scale...

N is any complete metric space and f is any uniformly continuous function from M to N, then there exists a unique uniformly continuous function f′ from...

as a bounding surface, ignoring its interior. In this light convex polytopes in p-space are equivalent to tilings of the (p−1)-sphere, while others may...

non-prismatic convex uniform 4-polytopes. There are two infinite sets of convex prismatic forms, along with 17 cases arising as prisms of the convex uniform polyhedra...

of [isometries of 3-space that preserve the tiling] is transitive on vertices). There are 28 convex examples in Euclidean 3-space, also called the Archimedean...

member of a uniformly equicontinuous set of functions is uniformly continuous, and every finite set of uniformly continuous functions is uniformly equicontinuous...

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

{M}},\mu )} be a positive measure space. A set Φ ⊂ L 1 ( μ ) {\displaystyle \Phi \subset L^{1}(\mu )} is called uniformly integrable if sup f ∈ Φ ‖ f ‖ L...

points that are nearly uniformly randomly distributed within a given convex body. The basic scheme of the algorithm is a nearly uniform sampling from within...

a topological vector space (not necessarily locally convex or Hausdorff) over the real or complex numbers. Then the open convex subsets of X {\displaystyle...

uniform honeycombs, such as the cubic honeycomb, which tessellate 3-space; similarly the 3D cube is related to the infinite 2D square tiling. Convex 4-polytopes...

a cube. It can be formed as the convex hull of the six axis-parallel unit vectors in three-dimensional Euclidean space. It is one of the five Platonic...