Perfect

Main forms: perfect, adjective.

Related forms: perfectness (extent to which something is perfect), perfection (being perfect)

Typical use:

• The best; something that cannot be improved further, something that fits the requirements exactly. Similar words: ideal, optimal
• Something pure, unsullied, without any tainting influences. Similar words: pure, ideal, isolated

Economics

In economics, perfect is typically used in the sense of ideal, or as good as it can get.

Perfect information (also called complete information): Perfect information refers to a situation in a game where, at any given time, every player has complete information about the game. Equivalently, there is no existing piece of information that can be given to a player to make that player play better. The term is used in economics to describe a situation where all people in an economic transaction or market, have complete information.

No related subject wiki entry.

Also located at: Wikipedia:Perfect information

Perfect competition (also called pure competition): A market form where no buyer or seller can perceptibly influence the price of the good. It usually occurs when there is a large pool of buyers, and a large number of competing sellers, for the same good.

Also located at: Wikipedia:Perfect competition, Britannica:Perfect competition

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.

Primary subject wiki entry: Topospaces:Perfectly normal space

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

In number theory

Perfect power: A natural number expressible as $a^{n}$, where $a,n$ are natural numbers and $n>1$

For $n=2$, termed a perfect square. For $n=3$, termed a perfect cube.

No relevant subject wiki entry.

Also located at: Wikipedia:Perfect power, Mathworld:PerfectPower

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

Primary subject wiki entry: Number:Perfect number

Also located at: Wikipedia:Perfect number, Mathworld:PerfectNumber, Planetmath:PerfectNumber

In field theory

Perfect field: A field that either has characteristic zero, or has characteristic $p$ and for which the map $x\mapsto x^{p}$ is a surjective map. Equivalently, it is a field such that every algebraic extension field for it is separable.

Primary subject wiki entry: Galois:Perfect field

Also located at: Mathworld:PerfectField, Planetmath:PerfectField

In graph theory

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

Term variations: Strongly perfect graph

No relevant subject wiki entry.

Also located at: Wikipedia:Perfect graph, Mathworld:PerfectGraph

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.

No relevant subject wiki entry.

In measure theory

Perfect measure