Adherent Point

An adherent point of a subset $S\subseteq X$ of a Topological Space $X$ is a point $x:X$ that can be approximated by staying within the subset $S$.

Explicitly, $x$ is an adherent point of $S$ if for every Open Neighborhood $x\in U\in\mathcal{O}({X})$, the intersection $U\cap S$ is Merely Inhabited.

Properties

• The adherent points of $S$ are precisely the Limit of Nets of points in $S$.

References

• https://ncatlab.org/nlab/show/limit+point