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 |
---|---|
Canonical name | AdherentPoint |
Date of creation | 2013-03-22 14:38:18 |
Last modified on | 2013-03-22 14:38:18 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 7 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 54A99 |