Definition:Set Derivative

It has been suggested that this page or section be merged into Definition:Derived Set. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mergeto}} from the code.

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

• 1989: Ryszard Engelking: General Topology (revised and completed ed.)

• Mizar article TOPGEN_1:def 3