Regular (mathematics)

In topology

Regular space: A topological space is termed regular if all points are closed sets (the $T_{1}$ assumption), and, given a point and a closed set not containing it, there are disjoint open sets containing the point and closed set respectively.

In some definitions, the $T_{1}$ assumption is skipped.

Related terms: regularity (the property of a topological space being regular)

Primary subject wiki entry: Topospaces:Regular space

Also located at: Wikipedia:Regular space, Planetmath:RegularSpace, Mathworld:RegularSpace

Regular covering

In differential geometry

Regular value

In the theory of differential equations

Regular singular point

In the theory of monoids and semigroups

Regular element in a semigroup: An element $a$ such that there exists $b$ satisfying $aba=a$.

Regular semigroup: A semigroup where every element is regular.

In group theory/representation theory

Regular group action

In geometry

Regular polygon: A polygon in the Euclidean plane is termed regular if all its sides have equal length and all its angles (the internal angles at its vertices) have equal measure.

No subject wiki entry.

Also located at Wikipedia:Regular polygon, Mathworld:RegularPolygon, Planetmath:RegularPolygon

Regular polyhedron

Regular polytope

In commutative algebra

Regular ring

Regular sequence

In algebraic geometry

Regular map

In number theory

Regular prime: A regular prime is a prime number $p$ that does not divide the class number of the cyclotomic field obtained by adjoining $p^{th}$ roots of unity to the field of rational numbers.

Pimary subject wiki entry: Number:Regular prime

Also located at Wikipedia:Regular prime, Mathworld:RegularPrime, Planetmath:RegularPrime

In graph theory

Regular graph

In axiomatic set theory

Regular cardinal

In measure theory

Regular measure

In category theory

Regular category