adherent point
Let be a topological space and be a subset. A point is an adherent point for if every open set containing contains at least one point of . A point is an adherent point for if and only if is in the closure of .
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 contains at least one point of different from .
References
- 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
Title | adherent point |
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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 |