Boundary (Topology)/Examples/Open 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 $\openint 0 1$ be the open unit interval in $\R$.


Then the boundary of $\openint 0 1$ is the set of its endpoints $\set {0, 1}$.


Sources

  • 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: Exercise $3.9: 31$
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