# Category:Pointwise Operations

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This category contains results about Pointwise Operations.

Definitions specific to this category can be found in Definitions/Pointwise Operations.

Let $S$ be a set.

Let $\struct {T, \circ}$ be an algebraic structure.

Let $T^S$ be the set of all mappings from $S$ to $T$.

Let $f, g \in T^S$, that is, let $f: S \to T$ and $g: S \to T$ be mappings.

Then the operation $f \oplus g$ is defined on $T^S$ as follows:

- $f \oplus g: S \to T: \forall x \in S: \map {\paren {f \oplus g} } x = \map f x \circ \map g x$

The operation $\oplus$ is called the **pointwise operation on $T^S$ induced by $\circ$**.

### Induced Structure

The algebraic structure $\struct {T^S, \oplus}$ is called the **algebraic structure on $T^S$ induced by $\circ$**.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### P

## Pages in category "Pointwise Operations"

The following 12 pages are in this category, out of 12 total.