Perfect (mathematics)

In group theory

Perfect group: A group that equals its own commutator subgroup (i.e. derived subgroup).

Main subject wiki entry: Groupprops:Perfect group

Also located at: Wikipedia:Perfect group, Mathworld:PerfectGroup, Planetmath:PerfectGroup

In topology

Perfect space: A topological space where every point is closed, and is an intersection of countably many open subsets containing it.

Main subject wiki entry: Topospaces:Perfect space Perfectly normal space: A normal space where every closed subset is an intersection of countably many open subsets containing it.

Perfect set: A set in a metric space that has no isolated points.

In number theory

Perfect power, for instance, perfect square or perfect cube: A perfect $n^{th}$ power is an integer that occurs as the $n^{th}$ power of an integer.

Perfect number: A natural number that equals the sum of all its proper divisors.

In field theory

Perfect field: A field that either has characteristic zero, or has $p$ and $x\mapsto x^{p}$ is a surjective map.

In graph theory

Perfect graph: A graph with the property that for every induced subgraph, the chromatic number equals the clique number.

Perfect matching: A matching in a bipartite graph such that every element on one side gets matched to exactly one element on the other side.

In measure theory

Perfect measure