Definition:Constant Mapping
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Definitions
A constant mapping or constant function is a mapping $f_c: S \to T$ defined as:
- $c \in T: f_c: S \to T: \forall x \in S: f_c \left({x}\right) = c$
That is, every element of $S$ is mapped to the same element $c$ in $T$.
In a certain sense, a constant mapping can be considered as a mapping which takes no arguments (see also arity).
Sources
- Richard A. Dean: Elements of Abstract Algebra (1966): $\S 0.4$: Example $11$
- George McCarty: Topology: An Introduction with Application to Topological Groups (1967): $\text{I}$
- W.A. Sutherland: Introduction to Metric and Topological Spaces (1975): Notation and Terminology
- Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (1993): $\S 1.6$
