Isolated_point

Definition

A point $a \in A$ is an isolated point of $A$ if it not a limit point of $A$.

As a word of caution, we need to be a little careful about how we understand the relationship between these concepts. Whereas an isolated point is always an element of the relevant set $A$, it is quite possible for a limit point of $A$ not to belong to $A$. As an example, consider the endpoint of an open interval. This situation is the subject of the next important definition.