Interior (Topology)/Examples/Closed Real Interval in Closed Unbounded Real Interval
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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:
- $S^\circ = \hointl a b$
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.7$: Definitions: Examples $3.7.25$