# Definition:Set Derivative

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## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A \subseteq S$.

The **derivative** of $A$ in $T$ is the set of all accumulation points of $A$.

It is usually denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ as $A'$.

## Also known as

The **set derivative** can also be referred to as the **derived set**.

It can also be denoted $\operatorname{Der} A$.

## Sources

- Mizar article TOPGEN_1:def 3