Updated: 12/01/2025
Dictionary Size: 121 terms
This 'dictionary' is a list of mathematical terms and my attempts at quick, no-nonsense definitions for them. Similar to the glossary, this is primarily a tool for my own use and many of the definitions will reflect this. Unlike the glossary, this resource is not supposed to give any explanations or examples beyond the definitions themselves - a group on this page is just a set with a binary operations which is associative, unital, and invertible.
If you have any requests for words to be added, or spot a typo, please let me know.
PDF copy of the dictionary compiled with LaTeX:here
PDF printout of flash-card version of the dictionary (may contain formatting errors due to longer entries - it's automated so I don't check every card)here
Entries marked ** have not been checked since I rewrote the dictionary software so may have typos
Abelian Group** Abelian Subalgebra** Algebra** Alternating** Associative** Axiom of Choice** Axiom of Extensionality** Axiom of Foundation** Axiom of Infinity** Axiom of Replacement** Axiom of the Pair Set**
Banach Space Basis (Linear Algebra)** Binary Product** Bound (Order Theory)** Bounded Set** Bundle (Topology)**
Cartesian Product** Category** Cauchy Complete** Cauchy Sequence** Chain (Order Theory)** Chain Complex** Class** Closed Ball** Closed Set** Coarse/Fine (Topology)** Co-Cone Category** Cokernel** Commutative** Commutative Ring** Commutator Lie Algebra** Compact (Topology)** Complement** Cone Category** Continuous (Topology)**
Diameter (Metric Space)** Differentiable Atlas Disjoint**
(Axiom of the) Empty Set** Equaliser** Equivalence Relation**
Fiber Bundle** Field** Fréchet Space (Functional Analysis)** Function** Functional Relation** Functor**
Graph (of a function or relation)** Group**
Hausdorff Space** Hom Set** Homeomorphism Horizontal Composition**
Ideal (Lie Algebra)** Ideal (Ring Theory)** Image (Homological Algebra)** Infimum** Initial Object** Intersection** Isomorphism**
Lie Algebra** Limit (Category Theory)** Limit (in a Metric Space)** Limit (in a Topological Space)** Linearly Independent** Local Ring Localization (of a Ring)
Manifold Maximal Ideal Maximal/Minimal Element** Metric Space** Metric Topology** Metrizable** Monoid**
Natural Transformation** Neighbourhood**
Paracompact Partial Order** Partition** (Axiom of the) Power Set** Product (Category Theory)** Product Topology** Proposition**
Reflexive** Relation** (Principle of) Restricted Comprehension** Ring**
Semigroup Semisimple Lie Algebra** Sequence** Set** Simple Lie Algebra** Span** Spectrum (of a Commutative Ring) Subalgebra** Subgroup Subset** Subset Product (Algebra)** Subspace Topology** Superset** Supremum** Symmetric Relation**
Terminal Object** Topological Field** Topological Space** Topological Vector Space** Total Order** Transitive**
(Axiom of) Union** Universal Enveloping Algebra**
Vector Space** Vertical Composition**