Perfect (mathematics): Difference between revisions
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===In group theory=== | ===In group theory=== | ||
{{:Perfect group}} | |||
===In topology=== | ===In topology=== | ||
{{:Perfect space}} | |||
[[Topospaces:Perfectly normal space|Perfectly normal space]]: A normal space where every closed subset is an intersection of countably many open subsets containing it. | [[Topospaces:Perfectly normal space|Perfectly normal space]]: A normal space where every closed subset is an intersection of countably many open subsets containing it. | ||
Revision as of 14:23, 16 May 2008
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 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.