[[Topology MOC]]
# Boundary
For a subset $S$ of a topological space $X$, the **boundary** $\partial S$ is the set of points that are neither the [[Interior and exterior|interior]] nor the [[Interior and exterior|exterior]], #m/def/topology
i.e. points in $X$ such that every open neighbourhood intersects both $S$ and $X \setminus S$.
Equivalently, it is the [[closure]] minus the [[Interior and exterior|interior]].

Using this definition, a set is open iff. it does not contain any of its boundary points.


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