Boundary (Topology)/Examples/Rationals in Closed Unit Interval

Examples of Boundaries in the context of Topology
Let $\struct {\R, \tau_d}$ be the real number line with the usual (Euclidean) topology. Let $S$ be the set defined as:
 * $S = \Q \cap \closedint 0 1$

where:
 * $\Q$ denotes the set of rational numbers
 * $\closedint 0 1$ denotes the closed unit interval.

Then the boundary of $S$ in $\struct {\R, \tau_d}$ is $\closedint 0 1$.