If $A$ is a finite set in $(\mathbb R, \mathfrak T_U)$ then $A' = \emptyset$.
My knowledge: $\mathfrak T_U$ is the usual topology
$A'$ is the set of all limit points and my definition for this is: Let $(X, \mathfrak T)$ be a topological space with $A \subseteq X$. A point $x$ in $X$ is said to be a limit point of $A$ provided that every open set containing $x$ contains a point $A$ different from $x$.
Does the set $A$ have to be closed in order for the set of limit points to be empty? That is my thought right now? So I am thinking I need to be looking for counterexample for this false conjecture?