Pointwise

In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value ${\displaystyle f(x)}$ of some function ${\displaystyle f.}$ An important class of pointwise concepts are the pointwise operations — operations defined on functions by applying the operations to function values separately for each point in the domain of definition. Important relations can also be defined pointwise.

Examples include

where ${\displaystyle f,g:X\to R}$.

See pointwise product, scalar.

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