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
D427: Isotone map
Children
D428: Antitone map
D468: Bijective map
D326: Cartesian product
D527: Composite map
D1519: Constant map
D3660: Countable map
D219: Empty map
D747: Idempotent map
D440: Identity map
D43: Inclusion map
D467: Injective map
D1492: Map graph
D528: Map image
D529: Map inverse image
D429: Monotone map
D2901: Multiset
D2660: Set endomorphism
D466: Surjective map