Interior (Topology)/Examples/Closed Real Interval in Closed Unbounded Real Interval

Examples of Interiors in the context of Topology
Let $\R$ be the real number line under the usual (Euclidean) metric.

Let $M$ be the subspace of $\R$ defined as:
 * $M = \hointl \gets b$

Let $S$ be the closed real interval defined as:
 * $S = \closedint a b$

Then the interior of $S$ in $M$ is given by:
 * $S^\circ = \hointr a b$