Topological Boundaries

Definition

Given a subset $A$ of a topological space, a point $x$ is said to be in the boundary of $A$ if $x$ is in iboth the closure of $A$ and the closure of the complement of $A$.

Notation

The boundary of a set $A$ in a topological space is denoted by $\Bdry(A)$. Other notation includes $\partial A$.