# adherent point

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 $x$.

## References

• 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
Title adherent point AdherentPoint 2013-03-22 14:38:18 2013-03-22 14:38:18 mathcam (2727) mathcam (2727) 7 mathcam (2727) Definition msc 54A99