List of mathematical objects
This is a list of mathematical objects, organized by branch.
List of mathematical objects by branch
[edit]- Groups
- Rings, Modules
- monoids
- Fields, Vector spaces
- Algebras
- Chain complexes
- Operations
- group-theoretic lattices, Order-theoretic lattices
- Continuous functions, Differentiable functions, Analytic functions
- Pathological functions
- Weierstrass function - Commonly used as an example of a continuous, nowhere-differentiable function
- Dirichlet function - Commonly used as an example of a nowhere continuous function
- Bump function - Commonly used as an example of a Non-analytic smooth function
- Derivative, Gradient
- Integral
- Jacobian matrix
Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory, proofs and theorems are also mathematical objects
- Points, Lines, Line segments,
- Polytopes, Regular polytopes
- Conic sections
- Spheres, Ellipsoids, Paraboloids, Hyperboloids,
- Cylinders, Cones
- Closed sets
- Filters
- Neighborhoods
- Nets
- Open sets
- Topological spaces
- Uniformities
- Manifolds
- Möbius strip, Klein bottle
- Cohomology groups
- Cohomotopy groups[1]
- Homology groups
- Homotopy groups
- Knots
- Holes
- Toruses
- Alexander horned sphere
References
[edit]- ^ Hu, Sze-Tsen (1971) [1959]. "Chapter VII. Cohomotopy Groups" (PDF). Homotopy theory (PDF). Academic Press. pp. 205–228. LCCN 59-11526. Retrieved August 28, 2024.