View source for Boundary

{{MSC|54A}}

The boundary of a subspace $A$ of a given [[topological space]] $X$ is the set of points of $X$ such that every [[neighbourhood]] of any point of it contains both points from $A$ and points from the complement $X\setminus A$. Equivalently, the points which are in the [[Interior of a set|interior]] neither of $A$ nor of $X \setminus A$; the set of points in the [[Closure of a set|closure]] of $A$ that are not in the interior of $A$. 

A subset $A$ is closed if it contains its boundary, and open if it is disjoint from its boundary.

The accepted notations include $\partial A$, $b(A)$, $\mathrm{Fr}(A)$, $\mathrm{Fr}_X(A)$.

Also: a synonym for the border of a [[manifold]], such as the border of a simplex.

====References====
* J.L. Kelley, "General topology", Graduate Texts in Mathematics '''27''' Springer (1975) {{ISBN|0-387-90125-6}} {{ZBL|0306.54002}}

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