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.

单词	AdherentPoint
释义	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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