adherent point
AdherentPoint
2004-09-24 12:49:29
2007-12-17 12:42:27
Definition
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Let $X$ be a topological space and $A\subset X$ be a subset. A point $x\in X$ is an \emph{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 $x$.
\begin{thebibliography}{9}
\bibitem{steen} L.A. Steen, J.A.Seebach, Jr.,
\emph{Counterexamples in topology},
Holt, Rinehart and Winston, Inc., 1970.
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