ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Definition D18
Map
Formulation 0
A D4: Binary relation $M = (X \times Y, f)$ is a map if and only if
(1) $\forall \, x \in X : \forall \, y, y' \in Y \, ((x, y), (x, y') \in f \quad \Rightarrow \quad y = y')$ (D358: Right-unique binary relation)
(2) $\forall \, x \in X : \exists \, y \in Y : (x, y) \in f$ (D359: Left-total binary relation)
Subdefinitions
Isotone map
Children
Antitone map
Bijective map
Cartesian product
Composite map
Constant map
Countable map
Empty map
Idempotent map
Identity map
Inclusion map
Injective map
Map graph
Map image
Map inverse image
Monotone map
Multiset
Set endomorphism
Surjective map