Metric Space is Open in Itself/Examples/Closed Real Interval
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Examples of Use of Metric Space is Open in Itself
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 $\closedint a b$.
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2$: Continuity generalized: metric spaces: $2.3$: Open sets in metric spaces: Example $2.3.10$