mathematical structure

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.

Observed surface forms (24)

• Lie group ×3
• integer sequence ×3
• causal structure representation ×2
• mathematical group ×2
• non-abelian group ×2
• symmetry group ×2
• topological space ×2
• *-algebra ×1
• algebraic structure ×1
• concept in convex analysis ×1

• construction in partition theory ×1
• finite group ×1
• fixed-point theory ×1
• formal logical system ×1
• group theory construction ×1
• mathematical theory ×1
• metric space ×1
• number system ×1
• ordered field ×1
• second-order logical system ×1
• set of mathematical conditions ×1
• set-theoretic construct ×1
• set-theoretic universe ×1
• unique factorization domain ×1

Instances (26)

• SU(2)_L via concept surface "Lie group"
• Schwarzschild Penrose diagram via concept surface "causal structure representation"
• Minkowski sum via concept surface "concept in convex analysis"
• von Neumann algebras
  surface form: von Neumann algebra
• von Neumann universe via concept surface "set-theoretic universe"
• Dyson’s transform in number theory via concept surface "construction in partition theory"
  surface form: Dyson’s transform
• Frege’s system in "Grundgesetze der Arithmetik" via concept surface "formal logical system"
• Hilbert spaces
  surface form: Hilbert space
• Euclidean space via concept surface "metric space"
• Gaussian integers via concept surface "unique factorization domain"
• Conway groups via concept surface "finite group"
  surface form: automorphism group of the Leech lattice
• Look-and-say sequence via concept surface "integer sequence"
• Monster group construction (with collaborators) via concept surface "group theory construction"
• Surreal numbers via concept surface "number system"
• Poincaré group via concept surface "mathematical group"
• Lorentz group via concept surface "mathematical group"
• Riemann surfaces via concept surface "topological space"
  surface form: Riemann surface
• Osterwalder–Schrader axioms via concept surface "set of mathematical conditions"
• Abelian groups via concept surface "algebraic structure"
  surface form: Abelian group
• Lorentzian geometry via concept surface "mathematical theory"
• Fibonacci sequence via concept surface "integer sequence"
• Kerr Penrose diagram via concept surface "causal structure representation"
• Kripke fixed-point theory of truth via concept surface "fixed-point theory"
• Ulam sequence via concept surface "integer sequence"
• Minkowski space-time
• Grothendieck universe via concept surface "set-theoretic construct"