▾ 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
Formulation 0
Let $X$ be a D11: Set.
A D18: Map $f : Y \to Z$ is an enclosed binary operation on $X$ if and only if
(1) $Y = X \times X$
(2) $Z \subseteq X$
Formulation 1
Let $X$ be a D11: Set.
A D554: Binary operation $f : X \times X \to Y$ on $X$ is enclosed if and only if \begin{equation} \forall \, x, y \in X : f(x, y) \in X \end{equation}
Formulation 2
Let $X$ be a D11: Set.
A D554: Binary operation $f : X \times X \to Y$ on $X$ is enclosed if and only if \begin{equation} Y \subseteq X \end{equation}
Also known as
Closed binary operation
Child definitions
» D734: Complex conjugation operation
» D263: Groupoid
» D379: Maximum operation
» D380: Minimum operation