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# 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.

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## Mathematics Subject Classification

54A99*no label found*

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