of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to...

In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures...

mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered...

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

put it more abstractly every seminormed vector space is a topological vector space and thus carries a topological structure which is induced by the semi-norm...

spaces Bounded set (topological vector space) – Generalization of boundedness PlanetMath entry for Locally Bounded nLab entry for Locally Bounded Category...

operator theory, a bounded linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological vector spaces (TVSs) X {\displaystyle...

analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get...

implies that a convex set in a real or complex topological vector space is path-connected (and therefore also connected). A set C is strictly convex if...

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

be called the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear...

claimed to be homeomorphic to the topological quotient. Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback...

ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations...

theorem. In topological vector spaces, a different definition for bounded sets exists which is sometimes called von Neumann boundedness. If the topology...

Metacompact space Noetherian topological space Orthocompact space Paracompact space Quasi-compact morphism Precompact set - also called totally bounded Relatively...

and only if it is a T1 space). A locally bounded topological vector space is a topological vector space that possesses a bounded neighborhood of the origin...

absolutely convex hull of a bounded set in a locally convex topological vector space is again bounded. If D {\displaystyle D} is a bounded disk in a TVS X {\displaystyle...

if it is complete as a topological vector space. If ( X , τ ) {\displaystyle (X,\tau )} is a metrizable topological vector space (such as any norm induced...

Look up bounded in Wiktionary, the free dictionary. Boundedness, bounded, or unbounded may refer to: Bounded rationality, the idea that human rationality...

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied...

analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order...

inherited by the function space. For example, the set of functions from any set X into a vector space has a natural vector space structure given by pointwise...

principal topological properties that distinguish topological spaces. A subset of a topological space X {\displaystyle X} is a connected set if it is a...

bilinear form Topological vector space, a blend of topological structure with the algebraic concept of a vector space A vector field is a vector-valued function...

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

Absolutely convex set – Convex and balanced set Absorbing set – Set that can be "inflated" to reach any point Bounded set (topological vector space) – Generalization...

set Balanced set – Construct in functional analysis Bornivorous set – A set that can absorb any bounded subset Bounded set (topological vector space) –...

bounded subset Bounded set (topological vector space) – Generalization of boundedness Locally convex topological vector space – Vector space with a topology...

Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that...

and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms...