Infrabarrelled space

In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the origin.

Version

v1 · 2026-09-28 · History

Domain-specific #

10057

Domain group

Formal Sciences

Origin domain

Mathematics

Subdomains

Functional Analysis, Topological Vector Spaces → Mathematics

Core Idea

Infrabarrelled space is treated here as the recurring crossdomainmodelsstructuresrepresentations identity summarized by this source-grounded definition: In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the origin. In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the origin.

Scope of Application

• Documented setting. In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the.

• Definition. A subset B of a topological vector space (TVS) X is called bornivorous if it absorbs all bounded subsets of X.

• Definition. that is, if for each bounded subset S of X, there exists some scalar r such that S \subseteq r B.

• Definition. A barrelled set or a barrel in a TVS is a set which is convex, balanced, absorbing and closed.

• Definition. A quasibarrelled space is a TVS for which every bornivorous barrelled set in the space is a neighbourhood of the origin.

Clarity

A clear use of Infrabarrelled space names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the origin.

Manages Complexity

Infrabarrelled space compresses multiple crossdomainmodelsstructuresrepresentations details into a stable diagnostic relation. The source shows both the central mechanism—that is, if for each bounded subset S of X, there exists some scalar r such that S \subseteq r B.—and the practical consequence—a Hausdorff topological vector space X is quasibarrelled if and only if every bounded closed linear operator from X into a complete metrizable TVS is continuous.

Abstract Reasoning

1. Type the carrier. Identify the crossdomainmodelsstructuresrepresentations entities to which the claim applies.
2. State the relation. Use the source-grounded identity: In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the origin.
3. Check operation and conditions. A barrelled set or a barrel in a TVS is a set which is convex, balanced, absorbing and closed.
4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Infrabarrelled space transfers literally when a new case preserves the same carrier type, relation, and recognition test. In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the origin. A subset B of a topological vector space (TVS) X is called bornivorous if it absorbs all bounded subsets of X. Beyond the home domain. No canonical parent is asserted for Infrabarrelled space.

Neighborhood in Abstraction Space

Infrabarrelled space sits in a sparse region of the domain-specific corpus (63^rd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Topological Vector Spaces (9 abstractions)

Nearest neighbors

• Countably quasi-barrelled space — 0.88
• Absolutely convex set — 0.86
• DF-space — 0.85
• Montel space — 0.85
• Directed algebraic topology — 0.83

Computed from structural-signature embeddings · 2026-10-08