Map kernel – TheoremDex

▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Operation
▾ N-operation
▾ Binary operation
▾ Enclosed binary operation
▾ Groupoid
▾ Semigroup
▾ Monoid

Map kernel

Formulation 0

Let $G$ be a D265: Monoid such that

(i)	$I_G$ is an D39: Identity element in $G$

Let $f : X \to G$ be a D18: Map.
The kernel of $f$ with respect to $G$ is the D11: Set \begin{equation} \{ x \in X : f(x) = I_G \} \end{equation}

Also known as

Kernel, Null space

Results