Let $X$ be a topological space and $A\subset X$ be a subset. A point $x\in X$ is an adherent point for $A$ if every open set containing $x$ contains at least one point of $A$. A point $x$ is an adherent point for $A$ if and only if $x$ is in the closure of $A$.

Note that this definition is slightly more general than that of a limit point, in that for a limit point it is required that every open set containing $x$ contains at least one point of $A$ different from $x$.