mathematical structure
C3748
concept
A mathematical structure is a set (or collection of objects) equipped with specified operations, relations, or properties that satisfy given axioms, providing a framework for studying abstract patterns and relationships.
All labels observed (48)
| Label | Occurrences |
|---|---|
| mathematical theory | 56 |
| Lie group | 24 |
| algebraic structure | 21 |
| mathematical group | 16 |
| mathematical structure canonical | 15 |
| integer sequence | 13 |
| topological space | 12 |
| mathematical framework | 9 |
| finite group | 8 |
| associative algebra | 7 |
| non-abelian group | 6 |
| combinatorial structure | 4 |
| dimension theory concept | 4 |
| symmetry group | 3 |
| category-theoretic structure | 2 |
| causal structure representation | 2 |
| formal logical system | 2 |
| metric space | 2 |
| noncommutative algebra | 2 |
| number system | 2 |
| ordered field | 2 |
| stability theory | 2 |
| structure in Hodge theory | 2 |
| structure in differential geometry | 2 |
| *-algebra | 1 |
| Steiner system | 1 |
| algebraic framework | 1 |
| categorical structure | 1 |
| concept in convex analysis | 1 |
| concept in discrete mathematics | 1 |
| construction in partition theory | 1 |
| fixed-point theory | 1 |
| group theory construction | 1 |
| information geometric structure | 1 |
| mathematical field | 1 |
| mathematical notion | 1 |
| mathematical structure in general relativity | 1 |
| model-theoretic construct | 1 |
| order-theoretic concept | 1 |
| order-theoretic structure | 1 |
| second-order logical system | 1 |
| set of mathematical conditions | 1 |
| set-theoretic construct | 1 |
| set-theoretic universe | 1 |
| structure in algebraic geometry | 1 |
| structure in classical field theory | 1 |
| structure in classical mechanics | 1 |
| unique factorization domain | 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: mathematical structure
Generated description
A mathematical structure is a set (or collection of objects) equipped with specified operations, relations, or properties that satisfy given axioms, providing a framework for studying abstract patterns and relationships.
Instances (220)
| Instance | Via concept surface |
|---|---|
| Teichmüller theory | mathematical theory |
| Fano plane | Steiner system |
|
Galois
surface form:
Galois connection
|
order-theoretic concept |
| Milnor K-theory | mathematical theory |
| Milnor–Thurston kneading theory | mathematical theory |
| Deligne–Lusztig theory | mathematical theory |
| Gelfand–Kirillov dimension | dimension theory concept |
| Gelfand–Levitan theory | mathematical theory |
|
Gelfand triples (rigged Hilbert spaces)
surface form:
Gelfand triple
|
— |
| C*-algebras | — |
| Gaussian integers | unique factorization domain |
|
Conway groups
surface form:
automorphism group of the Leech lattice
|
finite group |
| Look-and-say sequence | integer sequence |
| Monster group construction (with collaborators) | group theory construction |
| Surreal numbers | number system |
| Poincaré group | mathematical group |
| Kolmogorov–Arnold–Moser theory | mathematical theory |
| Lorentz group | mathematical group |
| twistor space | — |
|
highly composite numbers
surface form:
highly composite number
|
integer sequence |
| Iwasawa theory | mathematical theory |
| naive set theory | mathematical theory |
| quantum inverse scattering method | algebraic framework |
| Coxeter–Dynkin diagrams | combinatorial structure |
| Banach algebra | — |
| Littlewood–Paley theory | mathematical theory |
| Finite Operator Calculus | mathematical framework |
| Rota–Baxter algebra | algebraic structure |
|
rotation group SU(2)
surface form:
SU(2)
|
Lie group |
| Racah algebra | — |
| theory of divergent series | mathematical theory |
| global class field theory | mathematical theory |
| Du Bois-Reymond theory of orders of infinity | mathematical theory |
| Chandrasekhar’s theory of ellipsoidal figures of equilibrium | mathematical theory |
|
Riemann surfaces
surface form:
Riemann surface
|
topological space |
| p-adic numbers | number system |
| Kazhdan–Lusztig theory | mathematical theory |
|
semisimple Lie groups
surface form:
semisimple Lie group
|
Lie group |
| category theory | mathematical theory |
| ISO(n) | mathematical group |
| orthogonal group O(n) | mathematical group |
| affine group of R^n | mathematical group |
| theory of G-structures | mathematical theory |
|
special orthogonal group SO(n)
surface form:
SO(n)
|
mathematical group |
| Artin–Schreier theory | mathematical theory |
|
Lie algebras
surface form:
Lie algebra
|
algebraic structure |
|
universal enveloping algebras
surface form:
universal enveloping algebra
|
associative algebra |
| Calderón–Zygmund theory | mathematical theory |
| Hodge filtration | structure in Hodge theory |
| U(1) | mathematical group |