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...

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

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...

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

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

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

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...

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...

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...

mathematics, a barrelled space (also written barreled space) is a topological vector space (TVS) for which every barrelled set in the space is a neighbourhood...

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

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...

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...

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

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

Hausdorff then the closure of a compact set may fail to be compact (see footnote for example). In any topological vector space (TVS), a compact subset is complete...

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

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

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

subspaces of this space. Sequence spaces are typically equipped with a norm, or at least the structure of a topological vector space. The most important...

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

and topological structures underlie the linear topological space (in other words, topological vector space) structure. A linear topological space is both...

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...

Fréchet space: a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric. The space Qp of p-adic...

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

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

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...

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...