Function property

This article is about a general term. A list of important particular cases (instances) is available at Category:Function properties

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Function property, all facts related to Function property) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

Definition

A function property is a map from the collection of all possible functions from a group to itself, to the two-element set (true, false). A function which gets mapped to true is said to have the function property, and a function which gets mapped to false is said to not have the function property.

The function property must satisfy isomorphism-invariance: if $f_{1}:G\to G$ and $f_{2}:H\to H$ are functions, and there is an isomorphism $\sigma :G\to H$ such that $\sigma \circ f_{1}=f_{2}\circ \sigma$, then $f_{1}$ satisfies the function property iff $f_{2}$ satisfies the function property.