Editing Regular (section)

== Mathematics ==
=== Algebra and number theory ===
* [[Regular category]], a kind of category that has similarities to both Abelian categories and to the category of sets
* [[Regular chain]]s in computer algebra
* [[Regular element (disambiguation)]], certain kinds of elements of an algebraic structure
* [[Regular extension]] of fields
* [[Regular ideal]] (multiple definitions)
* [[Regular Lie group]]
* [[Regular matrix (disambiguation)]]
* [[Regular monomorphism]]s and [[regular epimorphism]]s, monomorphisms (resp. epimorphisms) which equalize (resp. coequalize) some parallel pair of morphisms
* [[Regular number]]s, numbers which evenly divide a power of 60
* [[Regular p-group]], a concept capturing some of the more important properties of abelian ''p''-groups, but general enough to include most "small" ''p''-groups
* [[Regular prime]], a prime number ''p'' > 2 that does not divide the class number of the ''p''-th cyclotomic field
* The [[regular representation]] of a group G, the linear representation afforded by the group action of G on itself
* [[Regular ring]], a ring such that all its localizations have Krull dimension equal to the minimal number of generators of the maximal ideal
** [[von Neumann regular ring]], or absolutely flat ring (unrelated to the previous sense)
* [[Regular semi-algebraic system]]s in computer algebra
* [[Regular semigroup]], related to the previous sense
* [[Semigroup with involution#.2A .E2.80.93 regular semigroups|*-regular semigroup]]

=== Analysis ===
* [[Borel regular measure]]
* Cauchy-regular function (or [[Cauchy-continuous function]],) a continuous function between metric spaces which preserves Cauchy sequences
* [[Regular function]]s, functions that are analytic and single-valued (unique) in a given region
* [[Regular measure]], a measure for which every measurable set is "approximately open" and "approximately closed"
* The [[regular part]], of a Laurent series, the series of terms with positive powers
* [[Regular singular point]]s, in theory of ordinary differential equations where the growth of solutions is bounded by an algebraic function
* Regularity, the [[differentiability class|degree of differentiability]] of a function
* Regularity conditions arise in the study of [[first-class constraint]]s in Hamiltonian mechanics
* [[elliptic operator#Elliptic regularity theorem|Regularity of an elliptic operator]]
* [[Regularity theory]] of [[elliptic partial differential equation]]s

=== Combinatorics, discrete math, and mathematical computer science ===
* [[Regular algebra]], or Kleene algebra
* [[Regular code]], an algebraic code with a uniform distribution of distances between codewords
* [[Regular expression]], a type of pattern describing a set of strings in computer science
* [[Regular graph]], a graph such that all the degrees of the vertices are equal
** [[Szemerédi regularity lemma]], some random behaviors in large graphs
* [[Regular language]], a formal language recognizable by a finite state automaton (related to the regular expression)
* [[Regular map (graph theory)]], a symmetric tessellation of a closed surface
* [[Regular matroid]], a matroid which can be represented over any field
* [[Regular paperfolding sequence]], also known as the dragon curve sequence
* [[Regular tree grammar]]

=== Geometry ===
* [[Castelnuovo–Mumford regularity]] of a coherent sheaf
* [[Closed regular set]]s in solid modeling
* [[Irregularity of a surface]] in algebraic geometry
* [[Regular curve]]s
* [[Regular grid]], a tesselation of Euclidean space by congruent bricks
* [[Regular map (algebraic geometry)]], a map between varieties given by polynomials
* Regular point, a [[singular point of an algebraic variety|non-singular point of an algebraic variety]]
* [[Regular point]] of a differentiable map, a point at which a map is a submersion
* [[Regular polygon]]s, polygons with all sides and angles equal
** [[Regular polyhedron]], a generalization of a regular polygon to higher dimensions
**[[Regular polytope]], a generalization of a regular polygon to higher dimensions
* [[Regular skew polyhedron]]

=== Logic, set theory, and foundations ===
* [[Axiom of Regularity]], also called the Axiom of Foundation, an axiom of set theory asserting the non-existence of certain infinite chains of sets
* [[Partition regularity]]
* [[Regular cardinal]], a cardinal number that is equal to its cofinality
* [[Regular modal logic]]

=== Probability and statistics ===
* [[Regular conditional probability]], a concept that has developed to overcome certain difficulties in formally defining conditional probabilities for continuous probability distributions
* Regular [[stochastic matrix]], a stochastic matrix such that all the entries of some power of the matrix are positive

=== Topology ===
* [[Free regular set]], a subset of a topological space that is acted upon disjointly under a given group action
* [[Regular homotopy]]
* [[Regular isotopy]] in knot theory, the equivalence relation of link diagrams that is generated by using the 2nd and 3rd Reidemeister moves only
* [[Regular space]] (or <math>T_3</math>) space, a topological space in which a point and a closed set can be separated by neighborhoods