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 $x$ .

Bibliography

1

L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.