Definition:Extension of Mapping

Definition
As a mapping is, by definition, also a relation, the definition is the same as that for an extension of a relation:

Let:


 * $$f_1 \subseteq X \times Y$$ be a mapping on $$X \times Y$$;
 * $$f_2 \subseteq S \times T$$ be a mapping on $$S \times T$$;
 * $$X \subseteq S$$;
 * $$Y \subseteq T$$;
 * $$f_2 \restriction_{X \times Y}$$ be the restriction of $$f_2$$ to $$X \times Y$$.

Let $$f_2 \restriction_{X \times Y} = f_1$$.

Then $$f_2$$ extends or is an extension of $$f_1$$.