Difference between revisions of "Perfect (mathematics)"
(New page: ===In group theory=== Perfect group: A group that equals its own commutator subgroup. ===In topology=== Perfect space: A topolo...)
Revision as of 01:45, 13 May 2008
In group theory
Perfect group: A group that equals its own commutator subgroup.
Perfect space: A topological space where every point is closed, and is an intersection of countably many open subsets containing it.
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 power is an integer that occurs as the 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 and 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.