adherent point


Let X be a topological spaceMathworldPlanetmath and AX be a subset. A point xX 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 closurePlanetmathPlanetmath of A.

Note that this definition is slightly more general than that of a limit pointPlanetmathPlanetmath, 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