Adherent point

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In mathematics, an adherent point is a slight generalization of the idea of a limit 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 contining 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 of A different from x.

[edit] References

  • L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, (1970) Holt, Rinehart and Winston, Inc..
  • This article incorporates material from Adherent point on PlanetMath, which is licensed under the GFDL.
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