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...

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...

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...

"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...

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

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

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

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...

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

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

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

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...

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

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...

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...

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...

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...

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...

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...

higher-dimensional Euclidean space is said to be in convex position or convex independent if none of the points can be represented as a convex combination of the...

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

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

{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...

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...

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

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

subset of Y . {\displaystyle Y.} Uniformly continuous extensions Suppose that f : D → Y {\displaystyle f:D\to Y} is a uniformly continuous map from a dense...

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...

of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star...