Definition:Zero Mapping/Vector Space

Definition

Let $Y$ be a vector space.

Let $S$ be a set.

Let $\mathbf 0_Y$ be the identity element of $Y$.

Suppose $\mathbf 0 : S \to Y$ is a mapping such that:

$\forall x \in S: \map {\mathbf 0} x = \mathbf 0_Y$

Then $\mathbf 0$ is referred to as the zero mapping.

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.1$: Continuous and linear maps. Linear transformations