Metric Space is Open in Itself/Examples

Examples of Use of Metric Space is Open in Itself

Closed Real Interval

Let $\R$ be the real number line considered as an Euclidean space.

Let $\closedint a b \subset \R$ be a closed interval of $\R$.

Then from Closed Real Interval is not Open Set, $\closedint a b$ is not an open set of $\R$.

However, if $\closedint a b$ is considered as a subspace of $\R$, then it is seen that $\closedint a b$ is an open set of $\closedint a b$.