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 |
|---|---|
| Pauli group | mathematical group |
| Kerr Penrose diagram | causal structure representation |
|
Hopf algebra (concept named after him)
surface form:
Hopf algebra
|
algebraic structure |
| Baire space | topological space |
| Baire space ω^ω | topological space |
| SL(2,R) | Lie group |
| Pesin theory | mathematical theory |
| Cremona group of the projective plane | mathematical group |
| Kripke fixed-point theory of truth | fixed-point theory |
| Sierpiński carpet | topological space |
| Witt group of quadratic forms | algebraic structure |
| Brauer group | algebraic structure |
| Langlands program | mathematical theory |
| local class field theory | mathematical theory |
| Scott topology | — |
| Bondi–Metzner–Sachs symmetry | mathematical structure in general relativity |
| BMS group | mathematical group |
| Arakelov theory | mathematical theory |
| Cohen–Macaulay ring | algebraic structure |
| Fourier restriction theory | mathematical theory |
| Clifford algebra | associative algebra |
| geometric algebra | mathematical framework |
| theory of uniform distribution modulo 1 | mathematical theory |
| Fisher–Rao metric | information geometric structure |
| Galois extension | mathematical notion |
| Vessiot theory of differential equations | mathematical theory |
| Ulam sequence | integer sequence |
| Busemann space | metric space |
| Donaldson theory | mathematical theory |
| metaplectic group | mathematical group |
| Minkowski space-time | — |
| Langlands classification | mathematical theory |
| GAGA | mathematical theory |
|
CG
surface form:
Cohomologie Galoisienne
|
mathematical theory |
| calculus ratiocinator | formal logical system |
| Boolean algebra | algebraic structure |
| Grothendieck ring | algebraic structure |
| Gabriel localization theory | mathematical theory |
| Drinfeld modules | algebraic structure |
| Drinfeld associators | algebraic structure |
| Drinfeld–Jimbo quantum groups | algebraic structure |
| Bose–Mesner algebra | algebraic structure |
| Tate’s non-archimedean uniformization of elliptic curves | mathematical theory |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
Lie group |
| Hurwitz group | finite group |
| SL(2,7) | finite group |
| PGL(2,7) | finite group |
| S5 | finite group |
| symmetric group S5 | finite group |
| Hecke algebra | associative algebra |