vector space

C3749

concept

A vector space is a set of objects called vectors, equipped with operations of vector addition and scalar multiplication that satisfy specific axioms such as associativity, commutativity, distributivity, and the existence of additive identities and inverses.

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All labels observed (9)

Label	Occurrences
topological vector space	5
Banach space	3
normed vector space	2
complex vector space	1
element of weight space	1
geometric space	1
test function space	1
vector space canonical	1
ℚ-vector space	1

Description generation (CDg)

The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.

Instruction

generate a one-sentence description for a given conceptual class.
# Response Format
Return only the sentence: "Description: [one-sentence description of the conceptional class]"

Input

Class: vector space

Generated description

A vector space is a set of objects called vectors, equipped with operations of vector addition and scalar multiplication that satisfy specific axioms such as associativity, commutativity, distributivity, and the existence of additive identities and inverses.

Instances (12)

Instance	Via concept surface
Gaussian rationals ℚ(i)	ℚ-vector space
Hilbert spaces surface form: Hilbert space	—
Euclidean space	geometric space
Sobolev spaces	topological vector space
Orlicz spaces	Banach space
Hardy space	Banach space
Weyl vector	element of weight space
Bourgain spaces	Banach space
sl(2,C)	complex vector space
Schwartz–Bruhat space	test function space
Banach spaces surface form: Banach space	topological vector space
Schwartz space	topological vector space