Definition:Domain (Set Theory)/Mapping

Definition

Let $f: S \to T$ be a mapping.

The domain of $f$ is the set $S$ and can be denoted $\operatorname{Dom} \left({f}\right)$.

In the context of mappings, the domain and the preimage of a mapping are the same set.

This definition is the same as that for the domain of a function.

Also known as

The domain of (usually) a mapping is called by some sources, for example T.S. Blyth: Set Theory and Abstract Algebra (1975), the departure set.

Others refer to it on occasion as the source, but this is not recommended as there are other uses for that term.

Also see

• Codomain
• Range

• Image
• Preimage

Sources

• Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 8$: Functions
• W.E. Deskins: Abstract Algebra (1964): $\S 1.3$
• J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 3.2$
• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 1$
• George McCarty: Topology: An Introduction with Application to Topological Groups (1967): $\text{I}$
• A.N. Kolmogorov and S.V. Fomin‎: Introductory Real Analysis (1968): $\S 1.3$
• Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 10$
• T.S. Blyth: Set Theory and Abstract Algebra (1975): $\S 4$
• W.A. Sutherland: Introduction to Metric and Topological Spaces (1975): Notation and Terminology
• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 7.1$
• Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 20$
• H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability (1996): Appendix $\text{A}.3$